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|---|---|---|---|---|
What is the total area of all shapes shown in the image? | 3569.87 | $\text{Equilateral triangle: } s=52 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 52^2 = 1170.87$
$\text{Right triangle: } a=47, b=34 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 47 \times 34 = 799.0$
$\text{Square: } s=40 \Rightarrow A=s^2=40^2=1600$ | null |
|
There are 3 shapes on a 10x10 grid. Which shape is closest to the pink equilateral_triangle? | (3, 7) | Target shape: pink equilateral_triangle at (1, 3)
Distance from target shape to blue circle at (6, 0): 8
Distance from target shape to red equilateral_triangle at (3, 7): 6
Closest shape is the red equilateral_triangle at (3, 7) with distance 6 | {
"closest_shape": {
"color": "red",
"grid_position": [
3,
7
],
"index": 1,
"shape": "equilateral_triangle"
},
"grid_size": 10,
"shapes": [
{
"color": "blue",
"grid_position": [
6,
0
],
"index": 0,
"shape": "circle"
},
{
"color": "red",
"grid_position": [
3,
7
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "pink",
"grid_position": [
1,
3
],
"index": 2,
"shape": "equilateral_triangle"
}
],
"target": {
"color": "pink",
"grid_position": [
1,
3
],
"index": 2,
"shape": "equilateral_triangle"
},
"target_index": 2
} |
|
What is the total area of all shapes shown in the image? | 2849.65 | $\text{Equilateral triangle: } s=70 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 70^2 = 2121.76$
$\text{Equilateral triangle: } s=41 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 41^2 = 727.89$ | null |
|
There are 2 shapes on a 6x6 grid. Which shape is closest to the red hexagon? | (0, 5) | Target shape: red hexagon at (2, 0)
Distance from target shape to pink square at (0, 5): 7
Closest shape is the pink square at (0, 5) with distance 7 | {
"closest_shape": {
"color": "pink",
"grid_position": [
0,
5
],
"index": 1,
"shape": "square"
},
"grid_size": 6,
"shapes": [
{
"color": "red",
"grid_position": [
2,
0
],
"index": 0,
"shape": "hexagon"
},
{
"color": "pink",
"grid_position": [
0,
5
],
"index": 1,
"shape": "square"
}
],
"target": {
"color": "red",
"grid_position": [
2,
0
],
"index": 0,
"shape": "hexagon"
},
"target_index": 0
} |
|
There are 3 shapes on a 10x10 grid. Which shape is closest to the green rectangle? | (5, 7) | Target shape: green rectangle at (7, 2)
Distance from target shape to purple rectangle at (3, 6): 8
Distance from target shape to pink trapezoid at (5, 7): 7
Closest shape is the pink trapezoid at (5, 7) with distance 7 | {
"closest_shape": {
"color": "pink",
"grid_position": [
5,
7
],
"index": 2,
"shape": "trapezoid"
},
"grid_size": 10,
"shapes": [
{
"color": "purple",
"grid_position": [
3,
6
],
"index": 0,
"shape": "rectangle"
},
{
"color": "green",
"grid_position": [
7,
2
],
"index": 1,
"shape": "rectangle"
},
{
"color": "pink",
"grid_position": [
5,
7
],
"index": 2,
"shape": "trapezoid"
}
],
"target": {
"color": "green",
"grid_position": [
7,
2
],
"index": 1,
"shape": "rectangle"
},
"target_index": 1
} |
|
There are 3 shapes on a 7x7 grid. Which shape is closest to the gray equilateral_triangle? | (2, 4) | Target shape: gray equilateral_triangle at (2, 6)
Distance from target shape to cyan equilateral_triangle at (2, 4): 2
Distance from target shape to pink hexagon at (5, 2): 7
Closest shape is the cyan equilateral_triangle at (2, 4) with distance 2 | {
"closest_shape": {
"color": "cyan",
"grid_position": [
2,
4
],
"index": 0,
"shape": "equilateral_triangle"
},
"grid_size": 7,
"shapes": [
{
"color": "cyan",
"grid_position": [
2,
4
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "gray",
"grid_position": [
2,
6
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "pink",
"grid_position": [
5,
2
],
"index": 2,
"shape": "hexagon"
}
],
"target": {
"color": "gray",
"grid_position": [
2,
6
],
"index": 1,
"shape": "equilateral_triangle"
},
"target_index": 1
} |
|
There are 7 shapes on a 10x10 grid. Which shape is closest to the purple hexagon? | (9, 4) | Target shape: purple hexagon at (8, 6)
Distance from target shape to brown square at (9, 4): 3
Distance from target shape to orange equilateral_triangle at (3, 8): 7
Distance from target shape to gray square at (2, 3): 9
Distance from target shape to cyan trapezoid at (5, 6): 3
Distance from target shape to green equilateral_triangle at (6, 7): 3
Distance from target shape to pink trapezoid at (9, 1): 6
Closest shape is the brown square at (9, 4) with distance 3 | {
"closest_shape": {
"color": "brown",
"grid_position": [
9,
4
],
"index": 0,
"shape": "square"
},
"grid_size": 10,
"shapes": [
{
"color": "brown",
"grid_position": [
9,
4
],
"index": 0,
"shape": "square"
},
{
"color": "orange",
"grid_position": [
3,
8
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "gray",
"grid_position": [
2,
3
],
"index": 2,
"shape": "square"
},
{
"color": "cyan",
"grid_position": [
5,
6
],
"index": 3,
"shape": "trapezoid"
},
{
"color": "green",
"grid_position": [
6,
7
],
"index": 4,
"shape": "equilateral_triangle"
},
{
"color": "purple",
"grid_position": [
8,
6
],
"index": 5,
"shape": "hexagon"
},
{
"color": "pink",
"grid_position": [
9,
1
],
"index": 6,
"shape": "trapezoid"
}
],
"target": {
"color": "purple",
"grid_position": [
8,
6
],
"index": 5,
"shape": "hexagon"
},
"target_index": 5
} |
|
There are 6 shapes on a 10x10 grid. Which shape is closest to the orange equilateral_triangle? | (6, 0) | Target shape: orange equilateral_triangle at (8, 1)
Distance from target shape to red rectangle at (5, 0): 4
Distance from target shape to green pentagon at (6, 0): 3
Distance from target shape to cyan equilateral_triangle at (5, 9): 11
Distance from target shape to brown equilateral_triangle at (3, 9): 13
Distance from target shape to blue right_triangle at (2, 7): 12
Closest shape is the green pentagon at (6, 0) with distance 3 | {
"closest_shape": {
"color": "green",
"grid_position": [
6,
0
],
"index": 1,
"shape": "pentagon"
},
"grid_size": 10,
"shapes": [
{
"color": "red",
"grid_position": [
5,
0
],
"index": 0,
"shape": "rectangle"
},
{
"color": "green",
"grid_position": [
6,
0
],
"index": 1,
"shape": "pentagon"
},
{
"color": "cyan",
"grid_position": [
5,
9
],
"index": 2,
"shape": "equilateral_triangle"
},
{
"color": "brown",
"grid_position": [
3,
9
],
"index": 3,
"shape": "equilateral_triangle"
},
{
"color": "blue",
"grid_position": [
2,
7
],
"index": 4,
"shape": "right_triangle"
},
{
"color": "orange",
"grid_position": [
8,
1
],
"index": 5,
"shape": "equilateral_triangle"
}
],
"target": {
"color": "orange",
"grid_position": [
8,
1
],
"index": 5,
"shape": "equilateral_triangle"
},
"target_index": 5
} |
|
What is the total area of all shapes shown in the image? | 18894.28 | $\text{Rectangle: } w=75, h=68 \Rightarrow A=w \times h = 75 \times 68 = 5100$
$\text{Rectangle: } w=52, h=68 \Rightarrow A=w \times h = 52 \times 68 = 3536$
$\text{Equilateral triangle: } s=43 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 43^2 = 800.64$
$\text{Pentagon: } s=32 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times32^2}{4\tan(\pi/5)} = 1761.77$
$\text{Circle: } r=23 \Rightarrow A=\pi \times r^2 = \pi \times 23^2 = 1661.9$
$\text{Trapezoid: } a=56, b=34, h=28 \Rightarrow A=\frac{a+b}2 \times h = \frac{56+34}2 \times 28 = 1260.0$
$\text{Hexagon: } s=36 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 36^2 = 3367.11$
$\text{Equilateral triangle: } s=57 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 57^2 = 1406.86$ | null |
|
What is the total area of all shapes shown in the image? | 3401.64 | $\text{Equilateral triangle: } s=43 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 43^2 = 800.64$
$\text{Square: } s=51 \Rightarrow A=s^2=51^2=2601$ | null |
|
There are 8 shapes on a 9x9 grid. Which shape is closest to the pink rectangle? | (5, 5) | Target shape: pink rectangle at (6, 4)
Distance from target shape to red hexagon at (6, 8): 4
Distance from target shape to purple pentagon at (4, 2): 4
Distance from target shape to gray trapezoid at (5, 5): 2
Distance from target shape to brown right_triangle at (8, 3): 3
Distance from target shape to cyan trapezoid at (7, 2): 3
Distance from target shape to green circle at (1, 4): 5
Distance from target shape to orange right_triangle at (6, 6): 2
Closest shape is the gray trapezoid at (5, 5) with distance 2 | {
"closest_shape": {
"color": "gray",
"grid_position": [
5,
5
],
"index": 3,
"shape": "trapezoid"
},
"grid_size": 9,
"shapes": [
{
"color": "red",
"grid_position": [
6,
8
],
"index": 0,
"shape": "hexagon"
},
{
"color": "purple",
"grid_position": [
4,
2
],
"index": 1,
"shape": "pentagon"
},
{
"color": "pink",
"grid_position": [
6,
4
],
"index": 2,
"shape": "rectangle"
},
{
"color": "gray",
"grid_position": [
5,
5
],
"index": 3,
"shape": "trapezoid"
},
{
"color": "brown",
"grid_position": [
8,
3
],
"index": 4,
"shape": "right_triangle"
},
{
"color": "cyan",
"grid_position": [
7,
2
],
"index": 5,
"shape": "trapezoid"
},
{
"color": "green",
"grid_position": [
1,
4
],
"index": 6,
"shape": "circle"
},
{
"color": "orange",
"grid_position": [
6,
6
],
"index": 7,
"shape": "right_triangle"
}
],
"target": {
"color": "pink",
"grid_position": [
6,
4
],
"index": 2,
"shape": "rectangle"
},
"target_index": 2
} |
|
What is the total area of all shapes shown in the image? | 12285.49 | $\text{Pentagon: } s=36 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times36^2}{4\tan(\pi/5)} = 2229.74$
$\text{Pentagon: } s=38 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times38^2}{4\tan(\pi/5)} = 2484.37$
$\text{Pentagon: } s=42 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times42^2}{4\tan(\pi/5)} = 3034.92$
$\text{Circle: } r=38 \Rightarrow A=\pi \times r^2 = \pi \times 38^2 = 4536.46$ | null |
|
What is the total area of all shapes shown in the image? | 14341.74 | $\text{Rectangle: } w=62, h=36 \Rightarrow A=w \times h = 62 \times 36 = 2232$
$\text{Rectangle: } w=57, h=63 \Rightarrow A=w \times h = 57 \times 63 = 3591$
$\text{Equilateral triangle: } s=72 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 72^2 = 2244.74$
$\text{Right triangle: } a=58, b=33 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 58 \times 33 = 957.0$
$\text{Circle: } r=33 \Rightarrow A=\pi \times r^2 = \pi \times 33^2 = 3421.19$
$\text{Right triangle: } a=47, b=45 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 47 \times 45 = 1057.5$
$\text{Equilateral triangle: } s=44 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 44^2 = 838.31$ | null |
|
What is the total area of all shapes shown in the image? | 3915.75 | $\text{Hexagon: } s=31 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 31^2 = 2496.75$
$\text{Rectangle: } w=43, h=33 \Rightarrow A=w \times h = 43 \times 33 = 1419$ | null |
|
There are 2 shapes on a 10x10 grid. Which shape is closest to the yellow hexagon? | (0, 4) | Target shape: yellow hexagon at (8, 9)
Distance from target shape to green equilateral_triangle at (0, 4): 13
Closest shape is the green equilateral_triangle at (0, 4) with distance 13 | {
"closest_shape": {
"color": "green",
"grid_position": [
0,
4
],
"index": 0,
"shape": "equilateral_triangle"
},
"grid_size": 10,
"shapes": [
{
"color": "green",
"grid_position": [
0,
4
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "yellow",
"grid_position": [
8,
9
],
"index": 1,
"shape": "hexagon"
}
],
"target": {
"color": "yellow",
"grid_position": [
8,
9
],
"index": 1,
"shape": "hexagon"
},
"target_index": 1
} |
|
There are 3 shapes on a 4x4 grid. Which shape is closest to the green trapezoid? | (1, 3) | Target shape: green trapezoid at (3, 3)
Distance from target shape to gray right_triangle at (1, 3): 2
Distance from target shape to orange square at (2, 2): 2
Closest shape is the gray right_triangle at (1, 3) with distance 2 | {
"closest_shape": {
"color": "gray",
"grid_position": [
1,
3
],
"index": 1,
"shape": "right_triangle"
},
"grid_size": 4,
"shapes": [
{
"color": "green",
"grid_position": [
3,
3
],
"index": 0,
"shape": "trapezoid"
},
{
"color": "gray",
"grid_position": [
1,
3
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "orange",
"grid_position": [
2,
2
],
"index": 2,
"shape": "square"
}
],
"target": {
"color": "green",
"grid_position": [
3,
3
],
"index": 0,
"shape": "trapezoid"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 10513.99 | $\text{Trapezoid: } a=40, b=41, h=36 \Rightarrow A=\frac{a+b}2 \times h = \frac{40+41}2 \times 36 = 1458.0$
$\text{Right triangle: } a=56, b=45 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 56 \times 45 = 1260.0$
$\text{Square: } s=53 \Rightarrow A=s^2=53^2=2809$
$\text{Trapezoid: } a=43, b=34, h=24 \Rightarrow A=\frac{a+b}2 \times h = \frac{43+34}2 \times 24 = 924.0$
$\text{Pentagon: } s=41 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times41^2}{4\tan(\pi/5)} = 2892.12$
$\text{Equilateral triangle: } s=52 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 52^2 = 1170.87$ | null |
|
There are 5 shapes on a 4x4 grid. Which shape is closest to the gray pentagon? | (3, 2) | Target shape: gray pentagon at (2, 3)
Distance from target shape to cyan pentagon at (0, 1): 4
Distance from target shape to purple trapezoid at (3, 2): 2
Distance from target shape to blue square at (2, 1): 2
Distance from target shape to brown circle at (0, 0): 5
Closest shape is the purple trapezoid at (3, 2) with distance 2 | {
"closest_shape": {
"color": "purple",
"grid_position": [
3,
2
],
"index": 1,
"shape": "trapezoid"
},
"grid_size": 4,
"shapes": [
{
"color": "cyan",
"grid_position": [
0,
1
],
"index": 0,
"shape": "pentagon"
},
{
"color": "purple",
"grid_position": [
3,
2
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "blue",
"grid_position": [
2,
1
],
"index": 2,
"shape": "square"
},
{
"color": "gray",
"grid_position": [
2,
3
],
"index": 3,
"shape": "pentagon"
},
{
"color": "brown",
"grid_position": [
0,
0
],
"index": 4,
"shape": "circle"
}
],
"target": {
"color": "gray",
"grid_position": [
2,
3
],
"index": 3,
"shape": "pentagon"
},
"target_index": 3
} |
|
There are 3 shapes on a 7x7 grid. Which shape is closest to the gray hexagon? | (2, 6) | Target shape: gray hexagon at (5, 5)
Distance from target shape to green equilateral_triangle at (4, 1): 5
Distance from target shape to pink pentagon at (2, 6): 4
Closest shape is the pink pentagon at (2, 6) with distance 4 | {
"closest_shape": {
"color": "pink",
"grid_position": [
2,
6
],
"index": 1,
"shape": "pentagon"
},
"grid_size": 7,
"shapes": [
{
"color": "green",
"grid_position": [
4,
1
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "pink",
"grid_position": [
2,
6
],
"index": 1,
"shape": "pentagon"
},
{
"color": "gray",
"grid_position": [
5,
5
],
"index": 2,
"shape": "hexagon"
}
],
"target": {
"color": "gray",
"grid_position": [
5,
5
],
"index": 2,
"shape": "hexagon"
},
"target_index": 2
} |
|
What is the total area of all shapes shown in the image? | 18110.17 | $\text{Circle: } r=23 \Rightarrow A=\pi \times r^2 = \pi \times 23^2 = 1661.9$
$\text{Pentagon: } s=40 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times40^2}{4\tan(\pi/5)} = 2752.76$
$\text{Equilateral triangle: } s=45 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 45^2 = 876.85$
$\text{Square: } s=65 \Rightarrow A=s^2=65^2=4225$
$\text{Equilateral triangle: } s=67 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 67^2 = 1943.79$
$\text{Rectangle: } w=79, h=59 \Rightarrow A=w \times h = 79 \times 59 = 4661$
$\text{Pentagon: } s=34 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times34^2}{4\tan(\pi/5)} = 1988.87$ | null |
|
What is the total area of all shapes shown in the image? | 31696.68 | $\text{Rectangle: } w=88, h=55 \Rightarrow A=w \times h = 88 \times 55 = 4840$
$\text{Square: } s=76 \Rightarrow A=s^2=76^2=5776$
$\text{Equilateral triangle: } s=55 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 55^2 = 1309.86$
$\text{Square: } s=66 \Rightarrow A=s^2=66^2=4356$
$\text{Pentagon: } s=37 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times37^2}{4\tan(\pi/5)} = 2355.33$
$\text{Square: } s=77 \Rightarrow A=s^2=77^2=5929$
$\text{Hexagon: } s=33 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 33^2 = 2829.3$
$\text{Pentagon: } s=50 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times50^2}{4\tan(\pi/5)} = 4301.19$ | null |
|
There are 2 shapes on a 8x8 grid. Which shape is closest to the yellow trapezoid? | (7, 7) | Target shape: yellow trapezoid at (1, 7)
Distance from target shape to green pentagon at (7, 7): 6
Closest shape is the green pentagon at (7, 7) with distance 6 | {
"closest_shape": {
"color": "green",
"grid_position": [
7,
7
],
"index": 1,
"shape": "pentagon"
},
"grid_size": 8,
"shapes": [
{
"color": "yellow",
"grid_position": [
1,
7
],
"index": 0,
"shape": "trapezoid"
},
{
"color": "green",
"grid_position": [
7,
7
],
"index": 1,
"shape": "pentagon"
}
],
"target": {
"color": "yellow",
"grid_position": [
1,
7
],
"index": 0,
"shape": "trapezoid"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 19523.24 | $\text{Square: } s=75 \Rightarrow A=s^2=75^2=5625$
$\text{Rectangle: } w=59, h=58 \Rightarrow A=w \times h = 59 \times 58 = 3422$
$\text{Square: } s=58 \Rightarrow A=s^2=58^2=3364$
$\text{Equilateral triangle: } s=51 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 51^2 = 1126.27$
$\text{Hexagon: } s=48 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 48^2 = 5985.97$ | null |
|
What is the total area of all shapes shown in the image? | 22010.38 | $\text{Trapezoid: } a=53, b=43, h=33 \Rightarrow A=\frac{a+b}2 \times h = \frac{53+43}2 \times 33 = 1584.0$
$\text{Rectangle: } w=71, h=39 \Rightarrow A=w \times h = 71 \times 39 = 2769$
$\text{Circle: } r=26 \Rightarrow A=\pi \times r^2 = \pi \times 26^2 = 2123.72$
$\text{Circle: } r=34 \Rightarrow A=\pi \times r^2 = \pi \times 34^2 = 3631.68$
$\text{Rectangle: } w=69, h=62 \Rightarrow A=w \times h = 69 \times 62 = 4278$
$\text{Trapezoid: } a=45, b=39, h=33 \Rightarrow A=\frac{a+b}2 \times h = \frac{45+39}2 \times 33 = 1386.0$
$\text{Hexagon: } s=49 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 49^2 = 6237.98$ | null |
|
There are 2 shapes on a 6x6 grid. Which shape is closest to the brown equilateral_triangle? | (4, 3) | Target shape: brown equilateral_triangle at (0, 0)
Distance from target shape to pink square at (4, 3): 7
Closest shape is the pink square at (4, 3) with distance 7 | {
"closest_shape": {
"color": "pink",
"grid_position": [
4,
3
],
"index": 1,
"shape": "square"
},
"grid_size": 6,
"shapes": [
{
"color": "brown",
"grid_position": [
0,
0
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "pink",
"grid_position": [
4,
3
],
"index": 1,
"shape": "square"
}
],
"target": {
"color": "brown",
"grid_position": [
0,
0
],
"index": 0,
"shape": "equilateral_triangle"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 3371.87 | $\text{Trapezoid: } a=47, b=37, h=35 \Rightarrow A=\frac{a+b}2 \times h = \frac{47+37}2 \times 35 = 1470.0$
$\text{Right triangle: } a=43, b=34 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 43 \times 34 = 731.0$
$\text{Equilateral triangle: } s=52 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 52^2 = 1170.87$ | null |
|
What is the total area of all shapes shown in the image? | 22208.0 | $\text{Rectangle: } w=98, h=64 \Rightarrow A=w \times h = 98 \times 64 = 6272$
$\text{Trapezoid: } a=42, b=46, h=20 \Rightarrow A=\frac{a+b}2 \times h = \frac{42+46}2 \times 20 = 880.0$
$\text{Hexagon: } s=34 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 34^2 = 3003.38$
$\text{Pentagon: } s=36 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times36^2}{4\tan(\pi/5)} = 2229.74$
$\text{Square: } s=64 \Rightarrow A=s^2=64^2=4096$
$\text{Hexagon: } s=44 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 44^2 = 5029.88$
$\text{Right triangle: } a=41, b=34 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 41 \times 34 = 697.0$ | null |
|
What is the total area of all shapes shown in the image? | 6917.1 | $\text{Right triangle: } a=58, b=50 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 58 \times 50 = 1450.0$
$\text{Pentagon: } s=37 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times37^2}{4\tan(\pi/5)} = 2355.33$
$\text{Right triangle: } a=54, b=50 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 54 \times 50 = 1350.0$
$\text{Pentagon: } s=32 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times32^2}{4\tan(\pi/5)} = 1761.77$ | null |
|
What is the total area of all shapes shown in the image? | 5492.94 | $\text{Equilateral triangle: } s=72 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 72^2 = 2244.74$
$\text{Pentagon: } s=38 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times38^2}{4\tan(\pi/5)} = 2484.37$
$\text{Equilateral triangle: } s=42 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 42^2 = 763.83$ | null |
|
There are 6 shapes on a 5x5 grid. Which shape is closest to the blue right_triangle? | (2, 3) | Target shape: blue right_triangle at (1, 3)
Distance from target shape to yellow pentagon at (2, 2): 2
Distance from target shape to gray pentagon at (2, 3): 1
Distance from target shape to orange rectangle at (3, 0): 5
Distance from target shape to red rectangle at (2, 1): 3
Distance from target shape to brown square at (3, 3): 2
Closest shape is the gray pentagon at (2, 3) with distance 1 | {
"closest_shape": {
"color": "gray",
"grid_position": [
2,
3
],
"index": 2,
"shape": "pentagon"
},
"grid_size": 5,
"shapes": [
{
"color": "yellow",
"grid_position": [
2,
2
],
"index": 0,
"shape": "pentagon"
},
{
"color": "blue",
"grid_position": [
1,
3
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "gray",
"grid_position": [
2,
3
],
"index": 2,
"shape": "pentagon"
},
{
"color": "orange",
"grid_position": [
3,
0
],
"index": 3,
"shape": "rectangle"
},
{
"color": "red",
"grid_position": [
2,
1
],
"index": 4,
"shape": "rectangle"
},
{
"color": "brown",
"grid_position": [
3,
3
],
"index": 5,
"shape": "square"
}
],
"target": {
"color": "blue",
"grid_position": [
1,
3
],
"index": 1,
"shape": "right_triangle"
},
"target_index": 1
} |
|
There are 6 shapes on a 3x3 grid. Which shape is closest to the gray hexagon? | (1, 2) | Target shape: gray hexagon at (2, 2)
Distance from target shape to yellow pentagon at (0, 1): 3
Distance from target shape to cyan pentagon at (2, 0): 2
Distance from target shape to green circle at (1, 1): 2
Distance from target shape to orange square at (1, 2): 1
Distance from target shape to brown pentagon at (0, 0): 4
Closest shape is the orange square at (1, 2) with distance 1 | {
"closest_shape": {
"color": "orange",
"grid_position": [
1,
2
],
"index": 4,
"shape": "square"
},
"grid_size": 3,
"shapes": [
{
"color": "yellow",
"grid_position": [
0,
1
],
"index": 0,
"shape": "pentagon"
},
{
"color": "gray",
"grid_position": [
2,
2
],
"index": 1,
"shape": "hexagon"
},
{
"color": "cyan",
"grid_position": [
2,
0
],
"index": 2,
"shape": "pentagon"
},
{
"color": "green",
"grid_position": [
1,
1
],
"index": 3,
"shape": "circle"
},
{
"color": "orange",
"grid_position": [
1,
2
],
"index": 4,
"shape": "square"
},
{
"color": "brown",
"grid_position": [
0,
0
],
"index": 5,
"shape": "pentagon"
}
],
"target": {
"color": "gray",
"grid_position": [
2,
2
],
"index": 1,
"shape": "hexagon"
},
"target_index": 1
} |
|
What is the total area of all shapes shown in the image? | 19247.23 | $\text{Rectangle: } w=53, h=57 \Rightarrow A=w \times h = 53 \times 57 = 3021$
$\text{Equilateral triangle: } s=64 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 64^2 = 1773.62$
$\text{Rectangle: } w=93, h=45 \Rightarrow A=w \times h = 93 \times 45 = 4185$
$\text{Square: } s=48 \Rightarrow A=s^2=48^2=2304$
$\text{Equilateral triangle: } s=67 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 67^2 = 1943.79$
$\text{Equilateral triangle: } s=63 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 63^2 = 1718.63$
$\text{Pentagon: } s=50 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times50^2}{4\tan(\pi/5)} = 4301.19$ | null |
|
There are 4 shapes on a 6x6 grid. Which shape is closest to the purple square? | (2, 3) | Target shape: purple square at (2, 2)
Distance from target shape to cyan equilateral_triangle at (0, 3): 3
Distance from target shape to red trapezoid at (0, 4): 4
Distance from target shape to blue trapezoid at (2, 3): 1
Closest shape is the blue trapezoid at (2, 3) with distance 1 | {
"closest_shape": {
"color": "blue",
"grid_position": [
2,
3
],
"index": 3,
"shape": "trapezoid"
},
"grid_size": 6,
"shapes": [
{
"color": "purple",
"grid_position": [
2,
2
],
"index": 0,
"shape": "square"
},
{
"color": "cyan",
"grid_position": [
0,
3
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "red",
"grid_position": [
0,
4
],
"index": 2,
"shape": "trapezoid"
},
{
"color": "blue",
"grid_position": [
2,
3
],
"index": 3,
"shape": "trapezoid"
}
],
"target": {
"color": "purple",
"grid_position": [
2,
2
],
"index": 0,
"shape": "square"
},
"target_index": 0
} |
|
There are 8 shapes on a 6x6 grid. Which shape is closest to the green equilateral_triangle? | (1, 2) | Target shape: green equilateral_triangle at (0, 0)
Distance from target shape to yellow rectangle at (0, 5): 5
Distance from target shape to gray equilateral_triangle at (4, 5): 9
Distance from target shape to red square at (1, 2): 3
Distance from target shape to blue rectangle at (2, 4): 6
Distance from target shape to pink rectangle at (1, 4): 5
Distance from target shape to cyan equilateral_triangle at (3, 2): 5
Distance from target shape to orange right_triangle at (3, 5): 8
Closest shape is the red square at (1, 2) with distance 3 | {
"closest_shape": {
"color": "red",
"grid_position": [
1,
2
],
"index": 2,
"shape": "square"
},
"grid_size": 6,
"shapes": [
{
"color": "yellow",
"grid_position": [
0,
5
],
"index": 0,
"shape": "rectangle"
},
{
"color": "gray",
"grid_position": [
4,
5
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "red",
"grid_position": [
1,
2
],
"index": 2,
"shape": "square"
},
{
"color": "green",
"grid_position": [
0,
0
],
"index": 3,
"shape": "equilateral_triangle"
},
{
"color": "blue",
"grid_position": [
2,
4
],
"index": 4,
"shape": "rectangle"
},
{
"color": "pink",
"grid_position": [
1,
4
],
"index": 5,
"shape": "rectangle"
},
{
"color": "cyan",
"grid_position": [
3,
2
],
"index": 6,
"shape": "equilateral_triangle"
},
{
"color": "orange",
"grid_position": [
3,
5
],
"index": 7,
"shape": "right_triangle"
}
],
"target": {
"color": "green",
"grid_position": [
0,
0
],
"index": 3,
"shape": "equilateral_triangle"
},
"target_index": 3
} |
|
What is the total area of all shapes shown in the image? | 10634.51 | $\text{Square: } s=72 \Rightarrow A=s^2=72^2=5184$
$\text{Square: } s=43 \Rightarrow A=s^2=43^2=1849$
$\text{Circle: } r=28 \Rightarrow A=\pi \times r^2 = \pi \times 28^2 = 2463.01$
$\text{Trapezoid: } a=52, b=47, h=23 \Rightarrow A=\frac{a+b}2 \times h = \frac{52+47}2 \times 23 = 1138.5$ | null |
|
There are 4 shapes on a 9x9 grid. Which shape is closest to the pink equilateral_triangle? | (5, 7) | Target shape: pink equilateral_triangle at (7, 6)
Distance from target shape to blue right_triangle at (4, 7): 4
Distance from target shape to yellow rectangle at (5, 7): 3
Distance from target shape to red right_triangle at (1, 5): 7
Closest shape is the yellow rectangle at (5, 7) with distance 3 | {
"closest_shape": {
"color": "yellow",
"grid_position": [
5,
7
],
"index": 1,
"shape": "rectangle"
},
"grid_size": 9,
"shapes": [
{
"color": "blue",
"grid_position": [
4,
7
],
"index": 0,
"shape": "right_triangle"
},
{
"color": "yellow",
"grid_position": [
5,
7
],
"index": 1,
"shape": "rectangle"
},
{
"color": "red",
"grid_position": [
1,
5
],
"index": 2,
"shape": "right_triangle"
},
{
"color": "pink",
"grid_position": [
7,
6
],
"index": 3,
"shape": "equilateral_triangle"
}
],
"target": {
"color": "pink",
"grid_position": [
7,
6
],
"index": 3,
"shape": "equilateral_triangle"
},
"target_index": 3
} |
|
There are 7 shapes on a 6x6 grid. Which shape is closest to the pink square? | (1, 5) | Target shape: pink square at (1, 4)
Distance from target shape to yellow equilateral_triangle at (0, 0): 5
Distance from target shape to green right_triangle at (4, 1): 6
Distance from target shape to cyan trapezoid at (1, 5): 1
Distance from target shape to red square at (5, 4): 4
Distance from target shape to brown rectangle at (0, 1): 4
Distance from target shape to orange circle at (0, 2): 3
Closest shape is the cyan trapezoid at (1, 5) with distance 1 | {
"closest_shape": {
"color": "cyan",
"grid_position": [
1,
5
],
"index": 2,
"shape": "trapezoid"
},
"grid_size": 6,
"shapes": [
{
"color": "yellow",
"grid_position": [
0,
0
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "green",
"grid_position": [
4,
1
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "cyan",
"grid_position": [
1,
5
],
"index": 2,
"shape": "trapezoid"
},
{
"color": "red",
"grid_position": [
5,
4
],
"index": 3,
"shape": "square"
},
{
"color": "brown",
"grid_position": [
0,
1
],
"index": 4,
"shape": "rectangle"
},
{
"color": "orange",
"grid_position": [
0,
2
],
"index": 5,
"shape": "circle"
},
{
"color": "pink",
"grid_position": [
1,
4
],
"index": 6,
"shape": "square"
}
],
"target": {
"color": "pink",
"grid_position": [
1,
4
],
"index": 6,
"shape": "square"
},
"target_index": 6
} |
|
There are 7 shapes on a 3x3 grid. Which shape is closest to the pink right_triangle? | (2, 2) | Target shape: pink right_triangle at (1, 2)
Distance from target shape to gray right_triangle at (2, 2): 1
Distance from target shape to brown trapezoid at (0, 0): 3
Distance from target shape to yellow circle at (1, 0): 2
Distance from target shape to cyan pentagon at (0, 1): 2
Distance from target shape to orange circle at (2, 1): 2
Distance from target shape to red trapezoid at (0, 2): 1
Closest shape is the gray right_triangle at (2, 2) with distance 1 | {
"closest_shape": {
"color": "gray",
"grid_position": [
2,
2
],
"index": 0,
"shape": "right_triangle"
},
"grid_size": 3,
"shapes": [
{
"color": "gray",
"grid_position": [
2,
2
],
"index": 0,
"shape": "right_triangle"
},
{
"color": "brown",
"grid_position": [
0,
0
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "yellow",
"grid_position": [
1,
0
],
"index": 2,
"shape": "circle"
},
{
"color": "cyan",
"grid_position": [
0,
1
],
"index": 3,
"shape": "pentagon"
},
{
"color": "orange",
"grid_position": [
2,
1
],
"index": 4,
"shape": "circle"
},
{
"color": "pink",
"grid_position": [
1,
2
],
"index": 5,
"shape": "right_triangle"
},
{
"color": "red",
"grid_position": [
0,
2
],
"index": 6,
"shape": "trapezoid"
}
],
"target": {
"color": "pink",
"grid_position": [
1,
2
],
"index": 5,
"shape": "right_triangle"
},
"target_index": 5
} |
|
There are 3 shapes on a 10x10 grid. Which shape is closest to the green equilateral_triangle? | (5, 8) | Target shape: green equilateral_triangle at (2, 4)
Distance from target shape to red rectangle at (5, 8): 7
Distance from target shape to orange circle at (9, 4): 7
Closest shape is the red rectangle at (5, 8) with distance 7 | {
"closest_shape": {
"color": "red",
"grid_position": [
5,
8
],
"index": 0,
"shape": "rectangle"
},
"grid_size": 10,
"shapes": [
{
"color": "red",
"grid_position": [
5,
8
],
"index": 0,
"shape": "rectangle"
},
{
"color": "orange",
"grid_position": [
9,
4
],
"index": 1,
"shape": "circle"
},
{
"color": "green",
"grid_position": [
2,
4
],
"index": 2,
"shape": "equilateral_triangle"
}
],
"target": {
"color": "green",
"grid_position": [
2,
4
],
"index": 2,
"shape": "equilateral_triangle"
},
"target_index": 2
} |
|
There are 8 shapes on a 10x10 grid. Which shape is closest to the blue trapezoid? | (3, 6) | Target shape: blue trapezoid at (3, 4)
Distance from target shape to orange trapezoid at (6, 9): 8
Distance from target shape to red equilateral_triangle at (8, 3): 6
Distance from target shape to cyan equilateral_triangle at (6, 0): 7
Distance from target shape to yellow rectangle at (1, 1): 5
Distance from target shape to purple rectangle at (3, 1): 3
Distance from target shape to brown equilateral_triangle at (3, 6): 2
Distance from target shape to gray circle at (0, 3): 4
Closest shape is the brown equilateral_triangle at (3, 6) with distance 2 | {
"closest_shape": {
"color": "brown",
"grid_position": [
3,
6
],
"index": 6,
"shape": "equilateral_triangle"
},
"grid_size": 10,
"shapes": [
{
"color": "orange",
"grid_position": [
6,
9
],
"index": 0,
"shape": "trapezoid"
},
{
"color": "red",
"grid_position": [
8,
3
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "blue",
"grid_position": [
3,
4
],
"index": 2,
"shape": "trapezoid"
},
{
"color": "cyan",
"grid_position": [
6,
0
],
"index": 3,
"shape": "equilateral_triangle"
},
{
"color": "yellow",
"grid_position": [
1,
1
],
"index": 4,
"shape": "rectangle"
},
{
"color": "purple",
"grid_position": [
3,
1
],
"index": 5,
"shape": "rectangle"
},
{
"color": "brown",
"grid_position": [
3,
6
],
"index": 6,
"shape": "equilateral_triangle"
},
{
"color": "gray",
"grid_position": [
0,
3
],
"index": 7,
"shape": "circle"
}
],
"target": {
"color": "blue",
"grid_position": [
3,
4
],
"index": 2,
"shape": "trapezoid"
},
"target_index": 2
} |
|
There are 6 shapes on a 5x5 grid. Which shape is closest to the gray square? | (0, 4) | Target shape: gray square at (1, 4)
Distance from target shape to blue equilateral_triangle at (1, 0): 4
Distance from target shape to red right_triangle at (0, 1): 4
Distance from target shape to cyan pentagon at (2, 1): 4
Distance from target shape to orange hexagon at (0, 4): 1
Distance from target shape to purple square at (1, 3): 1
Closest shape is the orange hexagon at (0, 4) with distance 1 | {
"closest_shape": {
"color": "orange",
"grid_position": [
0,
4
],
"index": 3,
"shape": "hexagon"
},
"grid_size": 5,
"shapes": [
{
"color": "blue",
"grid_position": [
1,
0
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "red",
"grid_position": [
0,
1
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "cyan",
"grid_position": [
2,
1
],
"index": 2,
"shape": "pentagon"
},
{
"color": "orange",
"grid_position": [
0,
4
],
"index": 3,
"shape": "hexagon"
},
{
"color": "gray",
"grid_position": [
1,
4
],
"index": 4,
"shape": "square"
},
{
"color": "purple",
"grid_position": [
1,
3
],
"index": 5,
"shape": "square"
}
],
"target": {
"color": "gray",
"grid_position": [
1,
4
],
"index": 4,
"shape": "square"
},
"target_index": 4
} |
|
What is the total area of all shapes shown in the image? | 5377.87 | $\text{Hexagon: } s=41 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 41^2 = 4367.37$
$\text{Right triangle: } a=43, b=47 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 43 \times 47 = 1010.5$ | null |
|
What is the total area of all shapes shown in the image? | 18306.42 | $\text{Rectangle: } w=91, h=46 \Rightarrow A=w \times h = 91 \times 46 = 4186$
$\text{Equilateral triangle: } s=43 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 43^2 = 800.64$
$\text{Right triangle: } a=46, b=50 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 46 \times 50 = 1150.0$
$\text{Rectangle: } w=58, h=40 \Rightarrow A=w \times h = 58 \times 40 = 2320$
$\text{Square: } s=75 \Rightarrow A=s^2=75^2=5625$
$\text{Pentagon: } s=32 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times32^2}{4\tan(\pi/5)} = 1761.77$
$\text{Circle: } r=28 \Rightarrow A=\pi \times r^2 = \pi \times 28^2 = 2463.01$ | null |
|
There are 8 shapes on a 6x6 grid. Which shape is closest to the purple circle? | (4, 1) | Target shape: purple circle at (3, 2)
Distance from target shape to orange circle at (2, 4): 3
Distance from target shape to yellow right_triangle at (4, 5): 4
Distance from target shape to blue rectangle at (5, 3): 3
Distance from target shape to cyan rectangle at (5, 1): 3
Distance from target shape to green equilateral_triangle at (4, 1): 2
Distance from target shape to gray equilateral_triangle at (0, 0): 5
Distance from target shape to brown rectangle at (5, 4): 4
Closest shape is the green equilateral_triangle at (4, 1) with distance 2 | {
"closest_shape": {
"color": "green",
"grid_position": [
4,
1
],
"index": 5,
"shape": "equilateral_triangle"
},
"grid_size": 6,
"shapes": [
{
"color": "orange",
"grid_position": [
2,
4
],
"index": 0,
"shape": "circle"
},
{
"color": "yellow",
"grid_position": [
4,
5
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "purple",
"grid_position": [
3,
2
],
"index": 2,
"shape": "circle"
},
{
"color": "blue",
"grid_position": [
5,
3
],
"index": 3,
"shape": "rectangle"
},
{
"color": "cyan",
"grid_position": [
5,
1
],
"index": 4,
"shape": "rectangle"
},
{
"color": "green",
"grid_position": [
4,
1
],
"index": 5,
"shape": "equilateral_triangle"
},
{
"color": "gray",
"grid_position": [
0,
0
],
"index": 6,
"shape": "equilateral_triangle"
},
{
"color": "brown",
"grid_position": [
5,
4
],
"index": 7,
"shape": "rectangle"
}
],
"target": {
"color": "purple",
"grid_position": [
3,
2
],
"index": 2,
"shape": "circle"
},
"target_index": 2
} |
|
There are 4 shapes on a 4x4 grid. Which shape is closest to the red square? | (1, 1) | Target shape: red square at (0, 0)
Distance from target shape to gray circle at (1, 1): 2
Distance from target shape to cyan hexagon at (0, 3): 3
Distance from target shape to pink rectangle at (1, 2): 3
Closest shape is the gray circle at (1, 1) with distance 2 | {
"closest_shape": {
"color": "gray",
"grid_position": [
1,
1
],
"index": 0,
"shape": "circle"
},
"grid_size": 4,
"shapes": [
{
"color": "gray",
"grid_position": [
1,
1
],
"index": 0,
"shape": "circle"
},
{
"color": "red",
"grid_position": [
0,
0
],
"index": 1,
"shape": "square"
},
{
"color": "cyan",
"grid_position": [
0,
3
],
"index": 2,
"shape": "hexagon"
},
{
"color": "pink",
"grid_position": [
1,
2
],
"index": 3,
"shape": "rectangle"
}
],
"target": {
"color": "red",
"grid_position": [
0,
0
],
"index": 1,
"shape": "square"
},
"target_index": 1
} |
|
There are 6 shapes on a 5x5 grid. Which shape is closest to the brown right_triangle? | (3, 1) | Target shape: brown right_triangle at (4, 0)
Distance from target shape to blue pentagon at (3, 1): 2
Distance from target shape to cyan square at (0, 0): 4
Distance from target shape to purple trapezoid at (1, 1): 4
Distance from target shape to gray right_triangle at (1, 3): 6
Distance from target shape to pink trapezoid at (1, 0): 3
Closest shape is the blue pentagon at (3, 1) with distance 2 | {
"closest_shape": {
"color": "blue",
"grid_position": [
3,
1
],
"index": 0,
"shape": "pentagon"
},
"grid_size": 5,
"shapes": [
{
"color": "blue",
"grid_position": [
3,
1
],
"index": 0,
"shape": "pentagon"
},
{
"color": "cyan",
"grid_position": [
0,
0
],
"index": 1,
"shape": "square"
},
{
"color": "purple",
"grid_position": [
1,
1
],
"index": 2,
"shape": "trapezoid"
},
{
"color": "gray",
"grid_position": [
1,
3
],
"index": 3,
"shape": "right_triangle"
},
{
"color": "pink",
"grid_position": [
1,
0
],
"index": 4,
"shape": "trapezoid"
},
{
"color": "brown",
"grid_position": [
4,
0
],
"index": 5,
"shape": "right_triangle"
}
],
"target": {
"color": "brown",
"grid_position": [
4,
0
],
"index": 5,
"shape": "right_triangle"
},
"target_index": 5
} |
|
There are 5 shapes on a 9x9 grid. Which shape is closest to the orange right_triangle? | (4, 5) | Target shape: orange right_triangle at (1, 5)
Distance from target shape to cyan trapezoid at (8, 7): 9
Distance from target shape to yellow trapezoid at (4, 5): 3
Distance from target shape to pink square at (5, 0): 9
Distance from target shape to purple right_triangle at (2, 0): 6
Closest shape is the yellow trapezoid at (4, 5) with distance 3 | {
"closest_shape": {
"color": "yellow",
"grid_position": [
4,
5
],
"index": 2,
"shape": "trapezoid"
},
"grid_size": 9,
"shapes": [
{
"color": "orange",
"grid_position": [
1,
5
],
"index": 0,
"shape": "right_triangle"
},
{
"color": "cyan",
"grid_position": [
8,
7
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "yellow",
"grid_position": [
4,
5
],
"index": 2,
"shape": "trapezoid"
},
{
"color": "pink",
"grid_position": [
5,
0
],
"index": 3,
"shape": "square"
},
{
"color": "purple",
"grid_position": [
2,
0
],
"index": 4,
"shape": "right_triangle"
}
],
"target": {
"color": "orange",
"grid_position": [
1,
5
],
"index": 0,
"shape": "right_triangle"
},
"target_index": 0
} |
|
There are 6 shapes on a 8x8 grid. Which shape is closest to the brown pentagon? | (3, 5) | Target shape: brown pentagon at (5, 6)
Distance from target shape to red rectangle at (3, 5): 3
Distance from target shape to cyan square at (7, 5): 3
Distance from target shape to orange square at (2, 0): 9
Distance from target shape to gray square at (4, 4): 3
Distance from target shape to blue square at (2, 7): 4
Closest shape is the red rectangle at (3, 5) with distance 3 | {
"closest_shape": {
"color": "red",
"grid_position": [
3,
5
],
"index": 1,
"shape": "rectangle"
},
"grid_size": 8,
"shapes": [
{
"color": "brown",
"grid_position": [
5,
6
],
"index": 0,
"shape": "pentagon"
},
{
"color": "red",
"grid_position": [
3,
5
],
"index": 1,
"shape": "rectangle"
},
{
"color": "cyan",
"grid_position": [
7,
5
],
"index": 2,
"shape": "square"
},
{
"color": "orange",
"grid_position": [
2,
0
],
"index": 3,
"shape": "square"
},
{
"color": "gray",
"grid_position": [
4,
4
],
"index": 4,
"shape": "square"
},
{
"color": "blue",
"grid_position": [
2,
7
],
"index": 5,
"shape": "square"
}
],
"target": {
"color": "brown",
"grid_position": [
5,
6
],
"index": 0,
"shape": "pentagon"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 26316.11 | $\text{Circle: } r=30 \Rightarrow A=\pi \times r^2 = \pi \times 30^2 = 2827.43$
$\text{Circle: } r=34 \Rightarrow A=\pi \times r^2 = \pi \times 34^2 = 3631.68$
$\text{Hexagon: } s=38 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 38^2 = 3751.62$
$\text{Right triangle: } a=58, b=39 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 58 \times 39 = 1131.0$
$\text{Hexagon: } s=50 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 50^2 = 6495.19$
$\text{Rectangle: } w=61, h=53 \Rightarrow A=w \times h = 61 \times 53 = 3233$
$\text{Pentagon: } s=50 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times50^2}{4\tan(\pi/5)} = 4301.19$
$\text{Right triangle: } a=54, b=35 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 54 \times 35 = 945.0$ | null |
|
What is the total area of all shapes shown in the image? | 21342.75 | $\text{Rectangle: } w=97, h=34 \Rightarrow A=w \times h = 97 \times 34 = 3298$
$\text{Trapezoid: } a=58, b=37, h=27 \Rightarrow A=\frac{a+b}2 \times h = \frac{58+37}2 \times 27 = 1282.5$
$\text{Right triangle: } a=48, b=47 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 48 \times 47 = 1128.0$
$\text{Rectangle: } w=76, h=55 \Rightarrow A=w \times h = 76 \times 55 = 4180$
$\text{Right triangle: } a=60, b=31 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 60 \times 31 = 930.0$
$\text{Equilateral triangle: } s=46 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 46^2 = 916.25$
$\text{Rectangle: } w=82, h=49 \Rightarrow A=w \times h = 82 \times 49 = 4018$
$\text{Rectangle: } w=86, h=65 \Rightarrow A=w \times h = 86 \times 65 = 5590$ | null |
|
What is the total area of all shapes shown in the image? | 10223.8 | $\text{Hexagon: } s=46 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 46^2 = 5497.53$
$\text{Equilateral triangle: } s=51 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 51^2 = 1126.27$
$\text{Square: } s=60 \Rightarrow A=s^2=60^2=3600$ | null |
|
There are 6 shapes on a 4x4 grid. Which shape is closest to the purple circle? | (2, 1) | Target shape: purple circle at (1, 1)
Distance from target shape to blue equilateral_triangle at (2, 1): 1
Distance from target shape to brown pentagon at (0, 1): 1
Distance from target shape to red pentagon at (1, 2): 1
Distance from target shape to gray equilateral_triangle at (0, 0): 2
Distance from target shape to orange trapezoid at (3, 2): 3
Closest shape is the blue equilateral_triangle at (2, 1) with distance 1 | {
"closest_shape": {
"color": "blue",
"grid_position": [
2,
1
],
"index": 0,
"shape": "equilateral_triangle"
},
"grid_size": 4,
"shapes": [
{
"color": "blue",
"grid_position": [
2,
1
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "brown",
"grid_position": [
0,
1
],
"index": 1,
"shape": "pentagon"
},
{
"color": "red",
"grid_position": [
1,
2
],
"index": 2,
"shape": "pentagon"
},
{
"color": "gray",
"grid_position": [
0,
0
],
"index": 3,
"shape": "equilateral_triangle"
},
{
"color": "orange",
"grid_position": [
3,
2
],
"index": 4,
"shape": "trapezoid"
},
{
"color": "purple",
"grid_position": [
1,
1
],
"index": 5,
"shape": "circle"
}
],
"target": {
"color": "purple",
"grid_position": [
1,
1
],
"index": 5,
"shape": "circle"
},
"target_index": 5
} |
|
There are 8 shapes on a 5x5 grid. Which shape is closest to the yellow square? | (3, 0) | Target shape: yellow square at (3, 1)
Distance from target shape to purple equilateral_triangle at (1, 4): 5
Distance from target shape to pink rectangle at (3, 0): 1
Distance from target shape to gray equilateral_triangle at (0, 4): 6
Distance from target shape to brown circle at (2, 4): 4
Distance from target shape to green square at (0, 2): 4
Distance from target shape to blue right_triangle at (4, 0): 2
Distance from target shape to cyan square at (1, 0): 3
Closest shape is the pink rectangle at (3, 0) with distance 1 | {
"closest_shape": {
"color": "pink",
"grid_position": [
3,
0
],
"index": 1,
"shape": "rectangle"
},
"grid_size": 5,
"shapes": [
{
"color": "purple",
"grid_position": [
1,
4
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "pink",
"grid_position": [
3,
0
],
"index": 1,
"shape": "rectangle"
},
{
"color": "gray",
"grid_position": [
0,
4
],
"index": 2,
"shape": "equilateral_triangle"
},
{
"color": "brown",
"grid_position": [
2,
4
],
"index": 3,
"shape": "circle"
},
{
"color": "green",
"grid_position": [
0,
2
],
"index": 4,
"shape": "square"
},
{
"color": "blue",
"grid_position": [
4,
0
],
"index": 5,
"shape": "right_triangle"
},
{
"color": "cyan",
"grid_position": [
1,
0
],
"index": 6,
"shape": "square"
},
{
"color": "yellow",
"grid_position": [
3,
1
],
"index": 7,
"shape": "square"
}
],
"target": {
"color": "yellow",
"grid_position": [
3,
1
],
"index": 7,
"shape": "square"
},
"target_index": 7
} |
|
What is the total area of all shapes shown in the image? | 6600.42 | $\text{Circle: } r=24 \Rightarrow A=\pi \times r^2 = \pi \times 24^2 = 1809.56$
$\text{Rectangle: } w=72, h=47 \Rightarrow A=w \times h = 72 \times 47 = 3384$
$\text{Equilateral triangle: } s=57 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 57^2 = 1406.86$ | null |
|
There are 5 shapes on a 4x4 grid. Which shape is closest to the purple circle? | (3, 2) | Target shape: purple circle at (3, 3)
Distance from target shape to yellow right_triangle at (1, 2): 3
Distance from target shape to gray circle at (3, 0): 3
Distance from target shape to green hexagon at (0, 0): 6
Distance from target shape to blue circle at (3, 2): 1
Closest shape is the blue circle at (3, 2) with distance 1 | {
"closest_shape": {
"color": "blue",
"grid_position": [
3,
2
],
"index": 4,
"shape": "circle"
},
"grid_size": 4,
"shapes": [
{
"color": "yellow",
"grid_position": [
1,
2
],
"index": 0,
"shape": "right_triangle"
},
{
"color": "purple",
"grid_position": [
3,
3
],
"index": 1,
"shape": "circle"
},
{
"color": "gray",
"grid_position": [
3,
0
],
"index": 2,
"shape": "circle"
},
{
"color": "green",
"grid_position": [
0,
0
],
"index": 3,
"shape": "hexagon"
},
{
"color": "blue",
"grid_position": [
3,
2
],
"index": 4,
"shape": "circle"
}
],
"target": {
"color": "purple",
"grid_position": [
3,
3
],
"index": 1,
"shape": "circle"
},
"target_index": 1
} |
|
There are 4 shapes on a 10x10 grid. Which shape is closest to the cyan rectangle? | (3, 3) | Target shape: cyan rectangle at (4, 3)
Distance from target shape to purple trapezoid at (3, 3): 1
Distance from target shape to orange square at (4, 2): 1
Distance from target shape to green hexagon at (6, 5): 4
Closest shape is the purple trapezoid at (3, 3) with distance 1 | {
"closest_shape": {
"color": "purple",
"grid_position": [
3,
3
],
"index": 1,
"shape": "trapezoid"
},
"grid_size": 10,
"shapes": [
{
"color": "cyan",
"grid_position": [
4,
3
],
"index": 0,
"shape": "rectangle"
},
{
"color": "purple",
"grid_position": [
3,
3
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "orange",
"grid_position": [
4,
2
],
"index": 2,
"shape": "square"
},
{
"color": "green",
"grid_position": [
6,
5
],
"index": 3,
"shape": "hexagon"
}
],
"target": {
"color": "cyan",
"grid_position": [
4,
3
],
"index": 0,
"shape": "rectangle"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 7672.28 | $\text{Rectangle: } w=50, h=50 \Rightarrow A=w \times h = 50 \times 50 = 2500$
$\text{Hexagon: } s=35 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 35^2 = 3182.64$
$\text{Trapezoid: } a=52, b=30, h=29 \Rightarrow A=\frac{a+b}2 \times h = \frac{52+30}2 \times 29 = 1189.0$
$\text{Equilateral triangle: } s=43 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 43^2 = 800.64$ | null |
|
What is the total area of all shapes shown in the image? | 17056.18 | $\text{Square: } s=53 \Rightarrow A=s^2=53^2=2809$
$\text{Pentagon: } s=45 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times45^2}{4\tan(\pi/5)} = 3483.97$
$\text{Hexagon: } s=43 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 43^2 = 4803.84$
$\text{Square: } s=54 \Rightarrow A=s^2=54^2=2916$
$\text{Right triangle: } a=57, b=37 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 57 \times 37 = 1054.5$
$\text{Pentagon: } s=34 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times34^2}{4\tan(\pi/5)} = 1988.87$ | null |
|
What is the total area of all shapes shown in the image? | 21377.85 | $\text{Trapezoid: } a=48, b=42, h=32 \Rightarrow A=\frac{a+b}2 \times h = \frac{48+42}2 \times 32 = 1440.0$
$\text{Trapezoid: } a=58, b=40, h=20 \Rightarrow A=\frac{a+b}2 \times h = \frac{58+40}2 \times 20 = 980.0$
$\text{Pentagon: } s=50 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times50^2}{4\tan(\pi/5)} = 4301.19$
$\text{Hexagon: } s=40 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 40^2 = 4156.92$
$\text{Square: } s=69 \Rightarrow A=s^2=69^2=4761$
$\text{Right triangle: } a=44, b=32 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 44 \times 32 = 704.0$
$\text{Rectangle: } w=55, h=51 \Rightarrow A=w \times h = 55 \times 51 = 2805$
$\text{Pentagon: } s=36 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times36^2}{4\tan(\pi/5)} = 2229.74$ | null |
|
What is the total area of all shapes shown in the image? | 19465.18 | $\text{Circle: } r=23 \Rightarrow A=\pi \times r^2 = \pi \times 23^2 = 1661.9$
$\text{Pentagon: } s=33 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times33^2}{4\tan(\pi/5)} = 1873.6$
$\text{Square: } s=58 \Rightarrow A=s^2=58^2=3364$
$\text{Square: } s=43 \Rightarrow A=s^2=43^2=1849$
$\text{Right triangle: } a=41, b=49 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 41 \times 49 = 1004.5$
$\text{Hexagon: } s=50 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 50^2 = 6495.19$
$\text{Circle: } r=32 \Rightarrow A=\pi \times r^2 = \pi \times 32^2 = 3216.99$ | null |
|
What is the total area of all shapes shown in the image? | 24875.12 | $\text{Circle: } r=39 \Rightarrow A=\pi \times r^2 = \pi \times 39^2 = 4778.36$
$\text{Right triangle: } a=49, b=44 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 49 \times 44 = 1078.0$
$\text{Trapezoid: } a=59, b=42, h=32 \Rightarrow A=\frac{a+b}2 \times h = \frac{59+42}2 \times 32 = 1616.0$
$\text{Rectangle: } w=89, h=57 \Rightarrow A=w \times h = 89 \times 57 = 5073$
$\text{Rectangle: } w=87, h=63 \Rightarrow A=w \times h = 87 \times 63 = 5481$
$\text{Square: } s=64 \Rightarrow A=s^2=64^2=4096$
$\text{Pentagon: } s=40 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times40^2}{4\tan(\pi/5)} = 2752.76$ | null |
|
What is the total area of all shapes shown in the image? | 16545.78 | $\text{Hexagon: } s=44 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 44^2 = 5029.88$
$\text{Circle: } r=28 \Rightarrow A=\pi \times r^2 = \pi \times 28^2 = 2463.01$
$\text{Square: } s=45 \Rightarrow A=s^2=45^2=2025$
$\text{Equilateral triangle: } s=41 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 41^2 = 727.89$
$\text{Rectangle: } w=100, h=63 \Rightarrow A=w \times h = 100 \times 63 = 6300$ | null |
|
There are 5 shapes on a 6x6 grid. Which shape is closest to the cyan right_triangle? | (2, 2) | Target shape: cyan right_triangle at (0, 1)
Distance from target shape to red circle at (3, 2): 4
Distance from target shape to pink square at (2, 2): 3
Distance from target shape to orange square at (2, 5): 6
Distance from target shape to brown trapezoid at (4, 3): 6
Closest shape is the pink square at (2, 2) with distance 3 | {
"closest_shape": {
"color": "pink",
"grid_position": [
2,
2
],
"index": 2,
"shape": "square"
},
"grid_size": 6,
"shapes": [
{
"color": "red",
"grid_position": [
3,
2
],
"index": 0,
"shape": "circle"
},
{
"color": "cyan",
"grid_position": [
0,
1
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "pink",
"grid_position": [
2,
2
],
"index": 2,
"shape": "square"
},
{
"color": "orange",
"grid_position": [
2,
5
],
"index": 3,
"shape": "square"
},
{
"color": "brown",
"grid_position": [
4,
3
],
"index": 4,
"shape": "trapezoid"
}
],
"target": {
"color": "cyan",
"grid_position": [
0,
1
],
"index": 1,
"shape": "right_triangle"
},
"target_index": 1
} |
|
There are 2 shapes on a 6x6 grid. Which shape is closest to the red circle? | (1, 4) | Target shape: red circle at (1, 1)
Distance from target shape to brown right_triangle at (1, 4): 3
Closest shape is the brown right_triangle at (1, 4) with distance 3 | {
"closest_shape": {
"color": "brown",
"grid_position": [
1,
4
],
"index": 0,
"shape": "right_triangle"
},
"grid_size": 6,
"shapes": [
{
"color": "brown",
"grid_position": [
1,
4
],
"index": 0,
"shape": "right_triangle"
},
{
"color": "red",
"grid_position": [
1,
1
],
"index": 1,
"shape": "circle"
}
],
"target": {
"color": "red",
"grid_position": [
1,
1
],
"index": 1,
"shape": "circle"
},
"target_index": 1
} |
|
There are 3 shapes on a 8x8 grid. Which shape is closest to the gray circle? | (7, 4) | Target shape: gray circle at (5, 4)
Distance from target shape to purple equilateral_triangle at (2, 7): 6
Distance from target shape to red trapezoid at (7, 4): 2
Closest shape is the red trapezoid at (7, 4) with distance 2 | {
"closest_shape": {
"color": "red",
"grid_position": [
7,
4
],
"index": 2,
"shape": "trapezoid"
},
"grid_size": 8,
"shapes": [
{
"color": "purple",
"grid_position": [
2,
7
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "gray",
"grid_position": [
5,
4
],
"index": 1,
"shape": "circle"
},
{
"color": "red",
"grid_position": [
7,
4
],
"index": 2,
"shape": "trapezoid"
}
],
"target": {
"color": "gray",
"grid_position": [
5,
4
],
"index": 1,
"shape": "circle"
},
"target_index": 1
} |
|
There are 7 shapes on a 10x10 grid. Which shape is closest to the yellow circle? | (5, 4) | Target shape: yellow circle at (5, 6)
Distance from target shape to cyan equilateral_triangle at (7, 3): 5
Distance from target shape to green trapezoid at (5, 4): 2
Distance from target shape to red pentagon at (4, 1): 6
Distance from target shape to orange circle at (6, 4): 3
Distance from target shape to blue hexagon at (9, 1): 9
Distance from target shape to brown pentagon at (2, 4): 5
Closest shape is the green trapezoid at (5, 4) with distance 2 | {
"closest_shape": {
"color": "green",
"grid_position": [
5,
4
],
"index": 1,
"shape": "trapezoid"
},
"grid_size": 10,
"shapes": [
{
"color": "cyan",
"grid_position": [
7,
3
],
"index": 0,
"shape": "equilateral_triangle"
},
{
"color": "green",
"grid_position": [
5,
4
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "red",
"grid_position": [
4,
1
],
"index": 2,
"shape": "pentagon"
},
{
"color": "orange",
"grid_position": [
6,
4
],
"index": 3,
"shape": "circle"
},
{
"color": "blue",
"grid_position": [
9,
1
],
"index": 4,
"shape": "hexagon"
},
{
"color": "brown",
"grid_position": [
2,
4
],
"index": 5,
"shape": "pentagon"
},
{
"color": "yellow",
"grid_position": [
5,
6
],
"index": 6,
"shape": "circle"
}
],
"target": {
"color": "yellow",
"grid_position": [
5,
6
],
"index": 6,
"shape": "circle"
},
"target_index": 6
} |
|
There are 3 shapes on a 3x3 grid. Which shape is closest to the green right_triangle? | (2, 1) | Target shape: green right_triangle at (0, 1)
Distance from target shape to pink rectangle at (2, 1): 2
Distance from target shape to blue right_triangle at (2, 0): 3
Closest shape is the pink rectangle at (2, 1) with distance 2 | {
"closest_shape": {
"color": "pink",
"grid_position": [
2,
1
],
"index": 0,
"shape": "rectangle"
},
"grid_size": 3,
"shapes": [
{
"color": "pink",
"grid_position": [
2,
1
],
"index": 0,
"shape": "rectangle"
},
{
"color": "green",
"grid_position": [
0,
1
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "blue",
"grid_position": [
2,
0
],
"index": 2,
"shape": "right_triangle"
}
],
"target": {
"color": "green",
"grid_position": [
0,
1
],
"index": 1,
"shape": "right_triangle"
},
"target_index": 1
} |
|
What is the total area of all shapes shown in the image? | 7298.0 | $\text{Trapezoid: } a=40, b=49, h=26 \Rightarrow A=\frac{a+b}2 \times h = \frac{40+49}2 \times 26 = 1157.0$
$\text{Rectangle: } w=89, h=69 \Rightarrow A=w \times h = 89 \times 69 = 6141$ | null |
|
What is the total area of all shapes shown in the image? | 6699.0 | $\text{Square: } s=72 \Rightarrow A=s^2=72^2=5184$
$\text{Trapezoid: } a=60, b=41, h=30 \Rightarrow A=\frac{a+b}2 \times h = \frac{60+41}2 \times 30 = 1515.0$ | null |
|
There are 3 shapes on a 4x4 grid. Which shape is closest to the purple square? | (1, 2) | Target shape: purple square at (1, 0)
Distance from target shape to green equilateral_triangle at (0, 2): 3
Distance from target shape to pink square at (1, 2): 2
Closest shape is the pink square at (1, 2) with distance 2 | {
"closest_shape": {
"color": "pink",
"grid_position": [
1,
2
],
"index": 2,
"shape": "square"
},
"grid_size": 4,
"shapes": [
{
"color": "purple",
"grid_position": [
1,
0
],
"index": 0,
"shape": "square"
},
{
"color": "green",
"grid_position": [
0,
2
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "pink",
"grid_position": [
1,
2
],
"index": 2,
"shape": "square"
}
],
"target": {
"color": "purple",
"grid_position": [
1,
0
],
"index": 0,
"shape": "square"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 12937.07 | $\text{Hexagon: } s=40 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 40^2 = 4156.92$
$\text{Hexagon: } s=37 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 37^2 = 3556.77$
$\text{Pentagon: } s=31 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times31^2}{4\tan(\pi/5)} = 1653.38$
$\text{Rectangle: } w=85, h=42 \Rightarrow A=w \times h = 85 \times 42 = 3570$ | null |
|
There are 4 shapes on a 3x3 grid. Which shape is closest to the red right_triangle? | (1, 1) | Target shape: red right_triangle at (2, 2)
Distance from target shape to purple hexagon at (0, 1): 3
Distance from target shape to blue circle at (1, 1): 2
Distance from target shape to green rectangle at (2, 0): 2
Closest shape is the blue circle at (1, 1) with distance 2 | {
"closest_shape": {
"color": "blue",
"grid_position": [
1,
1
],
"index": 2,
"shape": "circle"
},
"grid_size": 3,
"shapes": [
{
"color": "red",
"grid_position": [
2,
2
],
"index": 0,
"shape": "right_triangle"
},
{
"color": "purple",
"grid_position": [
0,
1
],
"index": 1,
"shape": "hexagon"
},
{
"color": "blue",
"grid_position": [
1,
1
],
"index": 2,
"shape": "circle"
},
{
"color": "green",
"grid_position": [
2,
0
],
"index": 3,
"shape": "rectangle"
}
],
"target": {
"color": "red",
"grid_position": [
2,
2
],
"index": 0,
"shape": "right_triangle"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 20501.0 | $\text{Square: } s=69 \Rightarrow A=s^2=69^2=4761$
$\text{Circle: } r=21 \Rightarrow A=\pi \times r^2 = \pi \times 21^2 = 1385.44$
$\text{Trapezoid: } a=47, b=32, h=25 \Rightarrow A=\frac{a+b}2 \times h = \frac{47+32}2 \times 25 = 987.5$
$\text{Hexagon: } s=30 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 30^2 = 2338.27$
$\text{Equilateral triangle: } s=43 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 43^2 = 800.64$
$\text{Square: } s=67 \Rightarrow A=s^2=67^2=4489$
$\text{Hexagon: } s=47 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 47^2 = 5739.15$ | null |
|
What is the total area of all shapes shown in the image? | 5553.82 | $\text{Hexagon: } s=35 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 35^2 = 3182.64$
$\text{Equilateral triangle: } s=74 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 74^2 = 2371.18$ | null |
|
What is the total area of all shapes shown in the image? | 22567.22 | $\text{Trapezoid: } a=47, b=35, h=20 \Rightarrow A=\frac{a+b}2 \times h = \frac{47+35}2 \times 20 = 820.0$
$\text{Rectangle: } w=94, h=44 \Rightarrow A=w \times h = 94 \times 44 = 4136$
$\text{Circle: } r=34 \Rightarrow A=\pi \times r^2 = \pi \times 34^2 = 3631.68$
$\text{Right triangle: } a=40, b=36 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 40 \times 36 = 720.0$
$\text{Pentagon: } s=48 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times48^2}{4\tan(\pi/5)} = 3963.98$
$\text{Rectangle: } w=61, h=54 \Rightarrow A=w \times h = 61 \times 54 = 3294$
$\text{Equilateral triangle: } s=78 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 78^2 = 2634.45$
$\text{Hexagon: } s=36 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 36^2 = 3367.11$ | null |
|
What is the total area of all shapes shown in the image? | 16207.43 | $\text{Rectangle: } w=40, h=36 \Rightarrow A=w \times h = 40 \times 36 = 1440$
$\text{Trapezoid: } a=55, b=48, h=22 \Rightarrow A=\frac{a+b}2 \times h = \frac{55+48}2 \times 22 = 1133.0$
$\text{Right triangle: } a=42, b=34 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 42 \times 34 = 714.0$
$\text{Rectangle: } w=68, h=66 \Rightarrow A=w \times h = 68 \times 66 = 4488$
$\text{Equilateral triangle: } s=80 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 80^2 = 2771.28$
$\text{Circle: } r=31 \Rightarrow A=\pi \times r^2 = \pi \times 31^2 = 3019.07$
$\text{Circle: } r=29 \Rightarrow A=\pi \times r^2 = \pi \times 29^2 = 2642.08$ | null |
|
What is the total area of all shapes shown in the image? | 10395.86 | $\text{Rectangle: } w=94, h=61 \Rightarrow A=w \times h = 94 \times 61 = 5734$
$\text{Trapezoid: } a=48, b=46, h=38 \Rightarrow A=\frac{a+b}2 \times h = \frac{48+46}2 \times 38 = 1786.0$
$\text{Equilateral triangle: } s=55 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 55^2 = 1309.86$
$\text{Trapezoid: } a=59, b=49, h=29 \Rightarrow A=\frac{a+b}2 \times h = \frac{59+49}2 \times 29 = 1566.0$ | null |
|
There are 6 shapes on a 4x4 grid. Which shape is closest to the cyan equilateral_triangle? | (2, 3) | Target shape: cyan equilateral_triangle at (1, 2)
Distance from target shape to red hexagon at (2, 3): 2
Distance from target shape to pink trapezoid at (2, 0): 3
Distance from target shape to green rectangle at (3, 1): 3
Distance from target shape to blue trapezoid at (0, 1): 2
Distance from target shape to gray rectangle at (3, 3): 3
Closest shape is the red hexagon at (2, 3) with distance 2 | {
"closest_shape": {
"color": "red",
"grid_position": [
2,
3
],
"index": 0,
"shape": "hexagon"
},
"grid_size": 4,
"shapes": [
{
"color": "red",
"grid_position": [
2,
3
],
"index": 0,
"shape": "hexagon"
},
{
"color": "pink",
"grid_position": [
2,
0
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "cyan",
"grid_position": [
1,
2
],
"index": 2,
"shape": "equilateral_triangle"
},
{
"color": "green",
"grid_position": [
3,
1
],
"index": 3,
"shape": "rectangle"
},
{
"color": "blue",
"grid_position": [
0,
1
],
"index": 4,
"shape": "trapezoid"
},
{
"color": "gray",
"grid_position": [
3,
3
],
"index": 5,
"shape": "rectangle"
}
],
"target": {
"color": "cyan",
"grid_position": [
1,
2
],
"index": 2,
"shape": "equilateral_triangle"
},
"target_index": 2
} |
|
What is the total area of all shapes shown in the image? | 6551.98 | $\text{Circle: } r=39 \Rightarrow A=\pi \times r^2 = \pi \times 39^2 = 4778.36$
$\text{Equilateral triangle: } s=64 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 64^2 = 1773.62$ | null |
|
What is the total area of all shapes shown in the image? | 17015.97 | $\text{Equilateral triangle: } s=63 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 63^2 = 1718.63$
$\text{Square: } s=41 \Rightarrow A=s^2=41^2=1681$
$\text{Pentagon: } s=48 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times48^2}{4\tan(\pi/5)} = 3963.98$
$\text{Rectangle: } w=98, h=64 \Rightarrow A=w \times h = 98 \times 64 = 6272$
$\text{Circle: } r=26 \Rightarrow A=\pi \times r^2 = \pi \times 26^2 = 2123.72$
$\text{Circle: } r=20 \Rightarrow A=\pi \times r^2 = \pi \times 20^2 = 1256.64$ | null |
|
What is the total area of all shapes shown in the image? | 18037.89 | $\text{Pentagon: } s=47 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times47^2}{4\tan(\pi/5)} = 3800.53$
$\text{Pentagon: } s=48 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times48^2}{4\tan(\pi/5)} = 3963.98$
$\text{Pentagon: } s=31 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times31^2}{4\tan(\pi/5)} = 1653.38$
$\text{Square: } s=61 \Rightarrow A=s^2=61^2=3721$
$\text{Rectangle: } w=71, h=69 \Rightarrow A=w \times h = 71 \times 69 = 4899$ | null |
|
What is the total area of all shapes shown in the image? | 8077.19 | $\text{Rectangle: } w=59, h=64 \Rightarrow A=w \times h = 59 \times 64 = 3776$
$\text{Pentagon: } s=50 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times50^2}{4\tan(\pi/5)} = 4301.19$ | null |
|
There are 2 shapes on a 5x5 grid. Which shape is closest to the brown circle? | (2, 2) | Target shape: brown circle at (1, 0)
Distance from target shape to blue hexagon at (2, 2): 3
Closest shape is the blue hexagon at (2, 2) with distance 3 | {
"closest_shape": {
"color": "blue",
"grid_position": [
2,
2
],
"index": 1,
"shape": "hexagon"
},
"grid_size": 5,
"shapes": [
{
"color": "brown",
"grid_position": [
1,
0
],
"index": 0,
"shape": "circle"
},
{
"color": "blue",
"grid_position": [
2,
2
],
"index": 1,
"shape": "hexagon"
}
],
"target": {
"color": "brown",
"grid_position": [
1,
0
],
"index": 0,
"shape": "circle"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 15713.49 | $\text{Right triangle: } a=50, b=46 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 50 \times 46 = 1150.0$
$\text{Rectangle: } w=74, h=51 \Rightarrow A=w \times h = 74 \times 51 = 3774$
$\text{Equilateral triangle: } s=54 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 54^2 = 1262.67$
$\text{Hexagon: } s=42 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 42^2 = 4583.01$
$\text{Equilateral triangle: } s=44 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 44^2 = 838.31$
$\text{Rectangle: } w=52, h=59 \Rightarrow A=w \times h = 52 \times 59 = 3068$
$\text{Trapezoid: } a=50, b=33, h=25 \Rightarrow A=\frac{a+b}2 \times h = \frac{50+33}2 \times 25 = 1037.5$ | null |
|
What is the total area of all shapes shown in the image? | 8801.85 | $\text{Equilateral triangle: } s=60 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 60^2 = 1558.85$
$\text{Square: } s=74 \Rightarrow A=s^2=74^2=5476$
$\text{Trapezoid: } a=43, b=50, h=38 \Rightarrow A=\frac{a+b}2 \times h = \frac{43+50}2 \times 38 = 1767.0$ | null |
|
What is the total area of all shapes shown in the image? | 20357.06 | $\text{Equilateral triangle: } s=58 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 58^2 = 1456.65$
$\text{Hexagon: } s=32 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 32^2 = 2660.43$
$\text{Pentagon: } s=40 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times40^2}{4\tan(\pi/5)} = 2752.76$
$\text{Trapezoid: } a=53, b=41, h=35 \Rightarrow A=\frac{a+b}2 \times h = \frac{53+41}2 \times 35 = 1645.0$
$\text{Square: } s=60 \Rightarrow A=s^2=60^2=3600$
$\text{Circle: } r=27 \Rightarrow A=\pi \times r^2 = \pi \times 27^2 = 2290.22$
$\text{Rectangle: } w=96, h=62 \Rightarrow A=w \times h = 96 \times 62 = 5952$ | null |
|
What is the total area of all shapes shown in the image? | 16223.64 | $\text{Right triangle: } a=42, b=47 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 42 \times 47 = 987.0$
$\text{Right triangle: } a=54, b=32 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 54 \times 32 = 864.0$
$\text{Rectangle: } w=99, h=56 \Rightarrow A=w \times h = 99 \times 56 = 5544$
$\text{Pentagon: } s=48 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times48^2}{4\tan(\pi/5)} = 3963.98$
$\text{Trapezoid: } a=48, b=43, h=37 \Rightarrow A=\frac{a+b}2 \times h = \frac{48+43}2 \times 37 = 1683.5$
$\text{Pentagon: } s=43 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times43^2}{4\tan(\pi/5)} = 3181.16$ | null |
|
There are 8 shapes on a 4x4 grid. Which shape is closest to the yellow hexagon? | (1, 0) | Target shape: yellow hexagon at (3, 0)
Distance from target shape to pink hexagon at (1, 0): 2
Distance from target shape to gray circle at (2, 2): 3
Distance from target shape to red rectangle at (0, 3): 6
Distance from target shape to orange right_triangle at (3, 2): 2
Distance from target shape to green hexagon at (0, 0): 3
Distance from target shape to cyan equilateral_triangle at (2, 1): 2
Distance from target shape to blue equilateral_triangle at (1, 3): 5
Closest shape is the pink hexagon at (1, 0) with distance 2 | {
"closest_shape": {
"color": "pink",
"grid_position": [
1,
0
],
"index": 0,
"shape": "hexagon"
},
"grid_size": 4,
"shapes": [
{
"color": "pink",
"grid_position": [
1,
0
],
"index": 0,
"shape": "hexagon"
},
{
"color": "gray",
"grid_position": [
2,
2
],
"index": 1,
"shape": "circle"
},
{
"color": "red",
"grid_position": [
0,
3
],
"index": 2,
"shape": "rectangle"
},
{
"color": "orange",
"grid_position": [
3,
2
],
"index": 3,
"shape": "right_triangle"
},
{
"color": "green",
"grid_position": [
0,
0
],
"index": 4,
"shape": "hexagon"
},
{
"color": "yellow",
"grid_position": [
3,
0
],
"index": 5,
"shape": "hexagon"
},
{
"color": "cyan",
"grid_position": [
2,
1
],
"index": 6,
"shape": "equilateral_triangle"
},
{
"color": "blue",
"grid_position": [
1,
3
],
"index": 7,
"shape": "equilateral_triangle"
}
],
"target": {
"color": "yellow",
"grid_position": [
3,
0
],
"index": 5,
"shape": "hexagon"
},
"target_index": 5
} |
|
There are 6 shapes on a 3x3 grid. Which shape is closest to the pink right_triangle? | (2, 1) | Target shape: pink right_triangle at (2, 2)
Distance from target shape to red rectangle at (0, 1): 3
Distance from target shape to cyan right_triangle at (2, 0): 2
Distance from target shape to brown pentagon at (1, 0): 3
Distance from target shape to green pentagon at (2, 1): 1
Distance from target shape to blue right_triangle at (0, 2): 2
Closest shape is the green pentagon at (2, 1) with distance 1 | {
"closest_shape": {
"color": "green",
"grid_position": [
2,
1
],
"index": 4,
"shape": "pentagon"
},
"grid_size": 3,
"shapes": [
{
"color": "red",
"grid_position": [
0,
1
],
"index": 0,
"shape": "rectangle"
},
{
"color": "cyan",
"grid_position": [
2,
0
],
"index": 1,
"shape": "right_triangle"
},
{
"color": "pink",
"grid_position": [
2,
2
],
"index": 2,
"shape": "right_triangle"
},
{
"color": "brown",
"grid_position": [
1,
0
],
"index": 3,
"shape": "pentagon"
},
{
"color": "green",
"grid_position": [
2,
1
],
"index": 4,
"shape": "pentagon"
},
{
"color": "blue",
"grid_position": [
0,
2
],
"index": 5,
"shape": "right_triangle"
}
],
"target": {
"color": "pink",
"grid_position": [
2,
2
],
"index": 2,
"shape": "right_triangle"
},
"target_index": 2
} |
|
There are 6 shapes on a 6x6 grid. Which shape is closest to the red square? | (1, 5) | Target shape: red square at (0, 3)
Distance from target shape to pink hexagon at (1, 5): 3
Distance from target shape to purple equilateral_triangle at (2, 0): 5
Distance from target shape to brown pentagon at (3, 5): 5
Distance from target shape to cyan right_triangle at (3, 2): 4
Distance from target shape to green square at (1, 0): 4
Closest shape is the pink hexagon at (1, 5) with distance 3 | {
"closest_shape": {
"color": "pink",
"grid_position": [
1,
5
],
"index": 0,
"shape": "hexagon"
},
"grid_size": 6,
"shapes": [
{
"color": "pink",
"grid_position": [
1,
5
],
"index": 0,
"shape": "hexagon"
},
{
"color": "purple",
"grid_position": [
2,
0
],
"index": 1,
"shape": "equilateral_triangle"
},
{
"color": "brown",
"grid_position": [
3,
5
],
"index": 2,
"shape": "pentagon"
},
{
"color": "cyan",
"grid_position": [
3,
2
],
"index": 3,
"shape": "right_triangle"
},
{
"color": "green",
"grid_position": [
1,
0
],
"index": 4,
"shape": "square"
},
{
"color": "red",
"grid_position": [
0,
3
],
"index": 5,
"shape": "square"
}
],
"target": {
"color": "red",
"grid_position": [
0,
3
],
"index": 5,
"shape": "square"
},
"target_index": 5
} |
|
There are 3 shapes on a 6x6 grid. Which shape is closest to the brown pentagon? | (4, 5) | Target shape: brown pentagon at (5, 4)
Distance from target shape to red trapezoid at (4, 5): 2
Distance from target shape to orange right_triangle at (2, 4): 3
Closest shape is the red trapezoid at (4, 5) with distance 2 | {
"closest_shape": {
"color": "red",
"grid_position": [
4,
5
],
"index": 1,
"shape": "trapezoid"
},
"grid_size": 6,
"shapes": [
{
"color": "brown",
"grid_position": [
5,
4
],
"index": 0,
"shape": "pentagon"
},
{
"color": "red",
"grid_position": [
4,
5
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "orange",
"grid_position": [
2,
4
],
"index": 2,
"shape": "right_triangle"
}
],
"target": {
"color": "brown",
"grid_position": [
5,
4
],
"index": 0,
"shape": "pentagon"
},
"target_index": 0
} |
|
What is the total area of all shapes shown in the image? | 6901 | $\text{Rectangle: } w=67, h=36 \Rightarrow A=w \times h = 67 \times 36 = 2412$
$\text{Square: } s=67 \Rightarrow A=s^2=67^2=4489$ | null |
|
What is the total area of all shapes shown in the image? | 23214.49 | $\text{Equilateral triangle: } s=77 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 77^2 = 2567.33$
$\text{Square: } s=68 \Rightarrow A=s^2=68^2=4624$
$\text{Right triangle: } a=55, b=44 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 55 \times 44 = 1210.0$
$\text{Circle: } r=21 \Rightarrow A=\pi \times r^2 = \pi \times 21^2 = 1385.44$
$\text{Rectangle: } w=59, h=35 \Rightarrow A=w \times h = 59 \times 35 = 2065$
$\text{Hexagon: } s=48 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 48^2 = 5985.97$
$\text{Hexagon: } s=31 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 31^2 = 2496.75$
$\text{Rectangle: } w=45, h=64 \Rightarrow A=w \times h = 45 \times 64 = 2880$ | null |
|
What is the total area of all shapes shown in the image? | 7251.46 | $\text{Right triangle: } a=47, b=40 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 47 \times 40 = 940.0$
$\text{Circle: } r=28 \Rightarrow A=\pi \times r^2 = \pi \times 28^2 = 2463.01$
$\text{Circle: } r=35 \Rightarrow A=\pi \times r^2 = \pi \times 35^2 = 3848.45$ | null |
|
What is the total area of all shapes shown in the image? | 9961.88 | $\text{Pentagon: } s=49 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times49^2}{4\tan(\pi/5)} = 4130.87$
$\text{Hexagon: } s=42 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 42^2 = 4583.01$
$\text{Trapezoid: } a=54, b=42, h=26 \Rightarrow A=\frac{a+b}2 \times h = \frac{54+42}2 \times 26 = 1248.0$ | null |
|
There are 6 shapes on a 8x8 grid. Which shape is closest to the blue pentagon? | (4, 1) | Target shape: blue pentagon at (4, 0)
Distance from target shape to green pentagon at (7, 7): 10
Distance from target shape to brown square at (4, 1): 1
Distance from target shape to gray circle at (6, 0): 2
Distance from target shape to yellow square at (2, 7): 9
Distance from target shape to cyan rectangle at (7, 6): 9
Closest shape is the brown square at (4, 1) with distance 1 | {
"closest_shape": {
"color": "brown",
"grid_position": [
4,
1
],
"index": 1,
"shape": "square"
},
"grid_size": 8,
"shapes": [
{
"color": "green",
"grid_position": [
7,
7
],
"index": 0,
"shape": "pentagon"
},
{
"color": "brown",
"grid_position": [
4,
1
],
"index": 1,
"shape": "square"
},
{
"color": "gray",
"grid_position": [
6,
0
],
"index": 2,
"shape": "circle"
},
{
"color": "blue",
"grid_position": [
4,
0
],
"index": 3,
"shape": "pentagon"
},
{
"color": "yellow",
"grid_position": [
2,
7
],
"index": 4,
"shape": "square"
},
{
"color": "cyan",
"grid_position": [
7,
6
],
"index": 5,
"shape": "rectangle"
}
],
"target": {
"color": "blue",
"grid_position": [
4,
0
],
"index": 3,
"shape": "pentagon"
},
"target_index": 3
} |
|
There are 5 shapes on a 5x5 grid. Which shape is closest to the gray trapezoid? | (0, 3) | Target shape: gray trapezoid at (0, 4)
Distance from target shape to green square at (1, 2): 3
Distance from target shape to yellow right_triangle at (2, 0): 6
Distance from target shape to pink equilateral_triangle at (0, 3): 1
Distance from target shape to purple right_triangle at (4, 3): 5
Closest shape is the pink equilateral_triangle at (0, 3) with distance 1 | {
"closest_shape": {
"color": "pink",
"grid_position": [
0,
3
],
"index": 3,
"shape": "equilateral_triangle"
},
"grid_size": 5,
"shapes": [
{
"color": "green",
"grid_position": [
1,
2
],
"index": 0,
"shape": "square"
},
{
"color": "gray",
"grid_position": [
0,
4
],
"index": 1,
"shape": "trapezoid"
},
{
"color": "yellow",
"grid_position": [
2,
0
],
"index": 2,
"shape": "right_triangle"
},
{
"color": "pink",
"grid_position": [
0,
3
],
"index": 3,
"shape": "equilateral_triangle"
},
{
"color": "purple",
"grid_position": [
4,
3
],
"index": 4,
"shape": "right_triangle"
}
],
"target": {
"color": "gray",
"grid_position": [
0,
4
],
"index": 1,
"shape": "trapezoid"
},
"target_index": 1
} |
|
What is the total area of all shapes shown in the image? | 5745.98 | $\text{Pentagon: } s=48 \Rightarrow A=\frac{5s^2}{4\tan(\pi/5)} = \frac{5\times48^2}{4\tan(\pi/5)} = 3963.98$
$\text{Right triangle: } a=54, b=31 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 54 \times 31 = 837.0$
$\text{Right triangle: } a=54, b=35 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 54 \times 35 = 945.0$ | null |
|
What is the total area of all shapes shown in the image? | 16114.93 | $\text{Hexagon: } s=31 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 31^2 = 2496.75$
$\text{Hexagon: } s=44 \Rightarrow A=\frac{3\sqrt{3}}2 \times s^2 = \frac{3\sqrt{3}}2 \times 44^2 = 5029.88$
$\text{Circle: } r=27 \Rightarrow A=\pi \times r^2 = \pi \times 27^2 = 2290.22$
$\text{Square: } s=51 \Rightarrow A=s^2=51^2=2601$
$\text{Circle: } r=27 \Rightarrow A=\pi \times r^2 = \pi \times 27^2 = 2290.22$
$\text{Equilateral triangle: } s=57 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 57^2 = 1406.86$ | null |
|
There are 2 shapes on a 10x10 grid. Which shape is closest to the pink rectangle? | (6, 4) | Target shape: pink rectangle at (9, 6)
Distance from target shape to orange pentagon at (6, 4): 5
Closest shape is the orange pentagon at (6, 4) with distance 5 | {
"closest_shape": {
"color": "orange",
"grid_position": [
6,
4
],
"index": 0,
"shape": "pentagon"
},
"grid_size": 10,
"shapes": [
{
"color": "orange",
"grid_position": [
6,
4
],
"index": 0,
"shape": "pentagon"
},
{
"color": "pink",
"grid_position": [
9,
6
],
"index": 1,
"shape": "rectangle"
}
],
"target": {
"color": "pink",
"grid_position": [
9,
6
],
"index": 1,
"shape": "rectangle"
},
"target_index": 1
} |
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