Dataset Viewer
image
imagewidth (px) 512
512
| problem
stringlengths 75
106
| solution
stringlengths 127
933
|
|---|---|---|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Right triangle: } a=6, b=2 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 6 \times 2 = 6.0$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$
$\text{Equilateral triangle: } s=8 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 8^2 = 27.71$
$\text{Square: } s=6 \Rightarrow A=s^2=6^2=36$
$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$</think>
<answer>173</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=3, h=8 \Rightarrow A=w \times h = 3 \times 8 = 24$
$\text{Right triangle: } a=5, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 5 \times 1 = 2.5$
$\text{Square: } s=4 \Rightarrow A=s^2=4^2=16$
$\text{Trapezoid: } a=6, b=4, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{6+4}2 \times 4 = 20.0$
$\text{Rectangle: } w=3, h=8 \Rightarrow A=w \times h = 3 \times 8 = 24$
$\text{Trapezoid: } a=4, b=6, h=9 \Rightarrow A=\frac{a+b}2 \times h = \frac{4+6}2 \times 9 = 45.0$</think>
<answer>132</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=7, b=6, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{7+6}2 \times 4 = 26.0$
$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$</think>
<answer>107</answer> |
|
There are 5 shapes on a 6x6 grid. Which shape is closest to the pink square? | <think>Target shape: pink square at (3, 5)
Distance from target shape to yellow rectangle at (2, 1): 5
Distance from target shape to red square at (5, 4): 3
Distance from target shape to blue right_triangle at (5, 3): 4
Distance from target shape to brown rectangle at (4, 1): 5
Closest shape is the red square at (5, 4) with distance 3</think>
<answer>(5, 4)</answer> |
|
There are 8 shapes on a 10x10 grid. Which shape is closest to the gray trapezoid? | <think>Target shape: gray trapezoid at (2, 2)
Distance from target shape to pink rectangle at (7, 2): 5
Distance from target shape to cyan right_triangle at (7, 1): 6
Distance from target shape to red trapezoid at (4, 9): 9
Distance from target shape to yellow equilateral_triangle at (5, 3): 4
Distance from target shape to blue square at (8, 4): 8
Distance from target shape to orange right_triangle at (6, 7): 9
Distance from target shape to purple square at (8, 0): 8
Closest shape is the yellow equilateral_triangle at (5, 3) with distance 4</think>
<answer>(5, 3)</answer> |
|
There are 5 shapes on a 3x3 grid. Which shape is closest to the green right_triangle? | <think>Target shape: green right_triangle at (2, 0)
Distance from target shape to red equilateral_triangle at (0, 1): 3
Distance from target shape to cyan trapezoid at (0, 2): 4
Distance from target shape to purple trapezoid at (1, 0): 1
Distance from target shape to orange rectangle at (1, 2): 3
Closest shape is the purple trapezoid at (1, 0) with distance 1</think>
<answer>(1, 0)</answer> |
|
There are 2 shapes on a 7x7 grid. Which shape is closest to the orange rectangle? | <think>Target shape: orange rectangle at (1, 0)
Distance from target shape to yellow equilateral_triangle at (6, 2): 7
Closest shape is the yellow equilateral_triangle at (6, 2) with distance 7</think>
<answer>(6, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=3, h=9 \Rightarrow A=w \times h = 3 \times 9 = 27$
$\text{Rectangle: } w=6, h=3 \Rightarrow A=w \times h = 6 \times 3 = 18$
$\text{Trapezoid: } a=2, b=6, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{2+6}2 \times 8 = 32.0$
$\text{Trapezoid: } a=1, b=7, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+7}2 \times 8 = 32.0$
$\text{Rectangle: } w=4, h=5 \Rightarrow A=w \times h = 4 \times 5 = 20$
$\text{Square: } s=7 \Rightarrow A=s^2=7^2=49$
$\text{Square: } s=8 \Rightarrow A=s^2=8^2=64$</think>
<answer>242</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=2 \Rightarrow A=s^2=2^2=4$
$\text{Equilateral triangle: } s=3 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 3^2 = 3.9$
$\text{Equilateral triangle: } s=4 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 4^2 = 6.93$
$\text{Trapezoid: } a=1, b=1, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+1}2 \times 4 = 4.0$
$\text{Right triangle: } a=4, b=7 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 7 = 14.0$
$\text{Trapezoid: } a=9, b=3, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{9+3}2 \times 4 = 24.0$</think>
<answer>57</answer> |
|
There are 5 shapes on a 4x4 grid. Which shape is closest to the green square? | <think>Target shape: green square at (0, 2)
Distance from target shape to orange right_triangle at (3, 2): 3
Distance from target shape to pink rectangle at (2, 2): 2
Distance from target shape to blue equilateral_triangle at (2, 1): 3
Distance from target shape to red trapezoid at (1, 1): 2
Closest shape is the pink rectangle at (2, 2) with distance 2</think>
<answer>(2, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=2, b=3, h=3 \Rightarrow A=\frac{a+b}2 \times h = \frac{2+3}2 \times 3 = 7.5$
$\text{Rectangle: } w=4, h=4 \Rightarrow A=w \times h = 4 \times 4 = 16$
$\text{Right triangle: } a=6, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 6 \times 9 = 27.0$
$\text{Square: } s=8 \Rightarrow A=s^2=8^2=64$</think>
<answer>114</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=7, b=5 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 7 \times 5 = 17.5$
$\text{Equilateral triangle: } s=1 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 1^2 = 0.43$
$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$</think>
<answer>99</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=9, h=2 \Rightarrow A=w \times h = 9 \times 2 = 18$
$\text{Rectangle: } w=3, h=2 \Rightarrow A=w \times h = 3 \times 2 = 6$
$\text{Equilateral triangle: } s=3 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 3^2 = 3.9$
$\text{Square: } s=2 \Rightarrow A=s^2=2^2=4$
$\text{Rectangle: } w=6, h=9 \Rightarrow A=w \times h = 6 \times 9 = 54$
$\text{Rectangle: } w=9, h=1 \Rightarrow A=w \times h = 9 \times 1 = 9$
$\text{Rectangle: } w=3, h=5 \Rightarrow A=w \times h = 3 \times 5 = 15$
$\text{Trapezoid: } a=1, b=6, h=3 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+6}2 \times 3 = 10.5$</think>
<answer>120</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=4 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 4^2 = 6.93$
$\text{Right triangle: } a=3, b=2 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 3 \times 2 = 3.0$</think>
<answer>10</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=7, h=7 \Rightarrow A=w \times h = 7 \times 7 = 49$
$\text{Trapezoid: } a=4, b=6, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{4+6}2 \times 7 = 35.0$
$\text{Right triangle: } a=6, b=4 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 6 \times 4 = 12.0$
$\text{Right triangle: } a=1, b=4 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 4 = 2.0$
$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$
$\text{Square: } s=5 \Rightarrow A=s^2=5^2=25$
$\text{Right triangle: } a=7, b=7 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 7 \times 7 = 24.5$
$\text{Rectangle: } w=8, h=5 \Rightarrow A=w \times h = 8 \times 5 = 40$</think>
<answer>188</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=5, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 5 \times 3 = 7.5$
$\text{Square: } s=4 \Rightarrow A=s^2=4^2=16$
$\text{Rectangle: } w=9, h=9 \Rightarrow A=w \times h = 9 \times 9 = 81$</think>
<answer>104</answer> |
|
There are 8 shapes on a 3x3 grid. Which shape is closest to the red rectangle? | <think>Target shape: red rectangle at (1, 1)
Distance from target shape to blue square at (2, 2): 2
Distance from target shape to gray square at (2, 1): 1
Distance from target shape to pink square at (1, 2): 1
Distance from target shape to brown rectangle at (0, 0): 2
Distance from target shape to yellow square at (2, 0): 2
Distance from target shape to cyan right_triangle at (0, 1): 1
Distance from target shape to orange rectangle at (0, 2): 2
Closest shape is the gray square at (2, 1) with distance 1</think>
<answer>(2, 1)</answer> |
|
There are 8 shapes on a 5x5 grid. Which shape is closest to the orange rectangle? | <think>Target shape: orange rectangle at (1, 4)
Distance from target shape to brown right_triangle at (0, 3): 2
Distance from target shape to purple right_triangle at (3, 1): 5
Distance from target shape to green square at (2, 1): 4
Distance from target shape to red right_triangle at (1, 2): 2
Distance from target shape to yellow right_triangle at (2, 4): 1
Distance from target shape to pink trapezoid at (3, 3): 3
Distance from target shape to blue rectangle at (0, 1): 4
Closest shape is the yellow right_triangle at (2, 4) with distance 1</think>
<answer>(2, 4)</answer> |
|
There are 3 shapes on a 9x9 grid. Which shape is closest to the brown rectangle? | <think>Target shape: brown rectangle at (5, 1)
Distance from target shape to pink right_triangle at (1, 8): 11
Distance from target shape to blue rectangle at (6, 8): 8
Closest shape is the blue rectangle at (6, 8) with distance 8</think>
<answer>(6, 8)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=5, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 5 \times 1 = 2.5$
$\text{Right triangle: } a=3, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 3 \times 9 = 13.5$
$\text{Trapezoid: } a=6, b=5, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{6+5}2 \times 7 = 38.5$
$\text{Right triangle: } a=2, b=7 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 2 \times 7 = 7.0$
$\text{Square: } s=8 \Rightarrow A=s^2=8^2=64$
$\text{Trapezoid: } a=2, b=1, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{2+1}2 \times 8 = 12.0$
$\text{Equilateral triangle: } s=8 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 8^2 = 27.71$</think>
<answer>165</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=9, h=1 \Rightarrow A=w \times h = 9 \times 1 = 9$
$\text{Rectangle: } w=2, h=9 \Rightarrow A=w \times h = 2 \times 9 = 18$
$\text{Trapezoid: } a=3, b=7, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+7}2 \times 8 = 40.0$
$\text{Rectangle: } w=7, h=8 \Rightarrow A=w \times h = 7 \times 8 = 56$</think>
<answer>123</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=2, b=8, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{2+8}2 \times 7 = 35.0$
$\text{Right triangle: } a=7, b=5 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 7 \times 5 = 17.5$
$\text{Rectangle: } w=2, h=4 \Rightarrow A=w \times h = 2 \times 4 = 8$
$\text{Rectangle: } w=4, h=1 \Rightarrow A=w \times h = 4 \times 1 = 4$
$\text{Equilateral triangle: } s=4 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 4^2 = 6.93$</think>
<answer>71</answer> |
|
There are 5 shapes on a 9x9 grid. Which shape is closest to the red square? | <think>Target shape: red square at (1, 6)
Distance from target shape to brown rectangle at (2, 0): 7
Distance from target shape to green right_triangle at (2, 3): 4
Distance from target shape to cyan square at (1, 8): 2
Distance from target shape to yellow right_triangle at (1, 3): 3
Closest shape is the cyan square at (1, 8) with distance 2</think>
<answer>(1, 8)</answer> |
|
There are 8 shapes on a 10x10 grid. Which shape is closest to the yellow right_triangle? | <think>Target shape: yellow right_triangle at (8, 6)
Distance from target shape to purple rectangle at (4, 2): 8
Distance from target shape to brown equilateral_triangle at (5, 6): 3
Distance from target shape to orange trapezoid at (7, 0): 7
Distance from target shape to green right_triangle at (4, 7): 5
Distance from target shape to cyan right_triangle at (9, 2): 5
Distance from target shape to pink equilateral_triangle at (6, 0): 8
Distance from target shape to red equilateral_triangle at (1, 2): 11
Closest shape is the brown equilateral_triangle at (5, 6) with distance 3</think>
<answer>(5, 6)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=9 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 9^2 = 35.07$
$\text{Rectangle: } w=6, h=9 \Rightarrow A=w \times h = 6 \times 9 = 54$
$\text{Rectangle: } w=2, h=6 \Rightarrow A=w \times h = 2 \times 6 = 12$
$\text{Trapezoid: } a=8, b=6, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{8+6}2 \times 7 = 49.0$
$\text{Right triangle: } a=1, b=2 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 2 = 1.0$
$\text{Right triangle: } a=6, b=8 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 6 \times 8 = 24.0$</think>
<answer>175</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=7, b=4 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 7 \times 4 = 14.0$
$\text{Right triangle: } a=5, b=5 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 5 \times 5 = 12.5$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$</think>
<answer>37</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=9 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 9^2 = 35.07$
$\text{Rectangle: } w=9, h=3 \Rightarrow A=w \times h = 9 \times 3 = 27$
$\text{Right triangle: } a=3, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 3 \times 3 = 4.5$
$\text{Rectangle: } w=4, h=8 \Rightarrow A=w \times h = 4 \times 8 = 32$</think>
<answer>99</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=3, h=4 \Rightarrow A=w \times h = 3 \times 4 = 12$
$\text{Rectangle: } w=4, h=3 \Rightarrow A=w \times h = 4 \times 3 = 12$
$\text{Right triangle: } a=2, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 2 \times 9 = 9.0$
$\text{Square: } s=5 \Rightarrow A=s^2=5^2=25$
$\text{Right triangle: } a=8, b=7 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 7 = 28.0$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$</think>
<answer>88</answer> |
|
There are 7 shapes on a 3x3 grid. Which shape is closest to the gray right_triangle? | <think>Target shape: gray right_triangle at (1, 2)
Distance from target shape to blue equilateral_triangle at (0, 1): 2
Distance from target shape to green square at (2, 1): 2
Distance from target shape to purple right_triangle at (1, 0): 2
Distance from target shape to red trapezoid at (2, 0): 3
Distance from target shape to pink trapezoid at (2, 2): 1
Distance from target shape to orange equilateral_triangle at (1, 1): 1
Closest shape is the pink trapezoid at (2, 2) with distance 1</think>
<answer>(2, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=4 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 4^2 = 6.93$
$\text{Trapezoid: } a=5, b=4, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+4}2 \times 6 = 27.0$
$\text{Right triangle: } a=3, b=5 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 3 \times 5 = 7.5$
$\text{Right triangle: } a=1, b=7 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 7 = 3.5$
$\text{Rectangle: } w=2, h=2 \Rightarrow A=w \times h = 2 \times 2 = 4$</think>
<answer>49</answer> |
|
There are 2 shapes on a 5x5 grid. Which shape is closest to the gray trapezoid? | <think>Target shape: gray trapezoid at (3, 4)
Distance from target shape to red square at (3, 0): 4
Closest shape is the red square at (3, 0) with distance 4</think>
<answer>(3, 0)</answer> |
|
There are 2 shapes on a 5x5 grid. Which shape is closest to the orange trapezoid? | <think>Target shape: orange trapezoid at (0, 3)
Distance from target shape to gray square at (4, 0): 7
Closest shape is the gray square at (4, 0) with distance 7</think>
<answer>(4, 0)</answer> |
|
There are 7 shapes on a 9x9 grid. Which shape is closest to the pink trapezoid? | <think>Target shape: pink trapezoid at (7, 0)
Distance from target shape to gray equilateral_triangle at (8, 7): 8
Distance from target shape to green rectangle at (4, 3): 6
Distance from target shape to yellow equilateral_triangle at (4, 8): 11
Distance from target shape to purple square at (8, 2): 3
Distance from target shape to blue trapezoid at (5, 8): 10
Distance from target shape to cyan square at (8, 3): 4
Closest shape is the purple square at (8, 2) with distance 3</think>
<answer>(8, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Rectangle: } w=1, h=8 \Rightarrow A=w \times h = 1 \times 8 = 8$
$\text{Trapezoid: } a=5, b=6, h=3 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+6}2 \times 3 = 16.5$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$
$\text{Trapezoid: } a=2, b=1, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{2+1}2 \times 6 = 9.0$
$\text{Rectangle: } w=3, h=6 \Rightarrow A=w \times h = 3 \times 6 = 18$</think>
<answer>67</answer> |
|
There are 4 shapes on a 3x3 grid. Which shape is closest to the cyan equilateral_triangle? | <think>Target shape: cyan equilateral_triangle at (1, 1)
Distance from target shape to pink trapezoid at (1, 2): 1
Distance from target shape to orange square at (0, 0): 2
Distance from target shape to gray right_triangle at (2, 0): 2
Closest shape is the pink trapezoid at (1, 2) with distance 1</think>
<answer>(1, 2)</answer> |
|
There are 8 shapes on a 7x7 grid. Which shape is closest to the orange trapezoid? | <think>Target shape: orange trapezoid at (4, 5)
Distance from target shape to blue right_triangle at (2, 5): 2
Distance from target shape to brown equilateral_triangle at (3, 3): 3
Distance from target shape to green rectangle at (5, 1): 5
Distance from target shape to pink trapezoid at (5, 3): 3
Distance from target shape to yellow right_triangle at (6, 6): 3
Distance from target shape to gray rectangle at (6, 5): 2
Distance from target shape to red rectangle at (1, 3): 5
Closest shape is the blue right_triangle at (2, 5) with distance 2</think>
<answer>(2, 5)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=8, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 9 = 36.0$
$\text{Right triangle: } a=1, b=2 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 2 = 1.0$
$\text{Square: } s=3 \Rightarrow A=s^2=3^2=9$
$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$</think>
<answer>47</answer> |
|
There are 3 shapes on a 5x5 grid. Which shape is closest to the blue right_triangle? | <think>Target shape: blue right_triangle at (1, 4)
Distance from target shape to brown square at (3, 2): 4
Distance from target shape to purple trapezoid at (2, 2): 3
Closest shape is the purple trapezoid at (2, 2) with distance 3</think>
<answer>(2, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$
$\text{Trapezoid: } a=5, b=1, h=9 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+1}2 \times 9 = 27.0$</think>
<answer>38</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=1, b=6, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+6}2 \times 7 = 24.5$
$\text{Rectangle: } w=1, h=3 \Rightarrow A=w \times h = 1 \times 3 = 3$
$\text{Equilateral triangle: } s=3 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 3^2 = 3.9$
$\text{Right triangle: } a=8, b=6 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 6 = 24.0$
$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Trapezoid: } a=5, b=6, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+6}2 \times 8 = 44.0$
$\text{Trapezoid: } a=8, b=1, h=1 \Rightarrow A=\frac{a+b}2 \times h = \frac{8+1}2 \times 1 = 4.5$
$\text{Right triangle: } a=7, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 7 \times 9 = 31.5$</think>
<answer>216</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=9, b=2, h=1 \Rightarrow A=\frac{a+b}2 \times h = \frac{9+2}2 \times 1 = 5.5$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$
$\text{Square: } s=6 \Rightarrow A=s^2=6^2=36$
$\text{Equilateral triangle: } s=7 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 7^2 = 21.22$</think>
<answer>64</answer> |
|
There are 8 shapes on a 3x3 grid. Which shape is closest to the pink rectangle? | <think>Target shape: pink rectangle at (0, 1)
Distance from target shape to purple equilateral_triangle at (2, 1): 2
Distance from target shape to orange square at (2, 2): 3
Distance from target shape to green rectangle at (2, 0): 3
Distance from target shape to blue trapezoid at (1, 2): 2
Distance from target shape to red trapezoid at (0, 0): 1
Distance from target shape to gray equilateral_triangle at (1, 0): 2
Distance from target shape to cyan rectangle at (1, 1): 1
Closest shape is the red trapezoid at (0, 0) with distance 1</think>
<answer>(0, 0)</answer> |
|
There are 3 shapes on a 3x3 grid. Which shape is closest to the orange rectangle? | <think>Target shape: orange rectangle at (0, 0)
Distance from target shape to pink equilateral_triangle at (1, 2): 3
Distance from target shape to brown equilateral_triangle at (2, 1): 3
Closest shape is the pink equilateral_triangle at (1, 2) with distance 3</think>
<answer>(1, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=1, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 1 = 0.5$
$\text{Right triangle: } a=4, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 1 = 2.0$</think>
<answer>2</answer> |
|
There are 5 shapes on a 4x4 grid. Which shape is closest to the green right_triangle? | <think>Target shape: green right_triangle at (1, 0)
Distance from target shape to yellow square at (2, 2): 3
Distance from target shape to purple right_triangle at (1, 2): 2
Distance from target shape to cyan right_triangle at (0, 3): 4
Distance from target shape to orange right_triangle at (3, 2): 4
Closest shape is the purple right_triangle at (1, 2) with distance 2</think>
<answer>(1, 2)</answer> |
|
There are 6 shapes on a 4x4 grid. Which shape is closest to the yellow square? | <think>Target shape: yellow square at (1, 0)
Distance from target shape to gray right_triangle at (2, 2): 3
Distance from target shape to pink trapezoid at (2, 3): 4
Distance from target shape to blue trapezoid at (2, 1): 2
Distance from target shape to brown right_triangle at (3, 2): 4
Distance from target shape to purple rectangle at (1, 1): 1
Closest shape is the purple rectangle at (1, 1) with distance 1</think>
<answer>(1, 1)</answer> |
|
There are 3 shapes on a 7x7 grid. Which shape is closest to the purple equilateral_triangle? | <think>Target shape: purple equilateral_triangle at (4, 0)
Distance from target shape to yellow rectangle at (2, 3): 5
Distance from target shape to orange trapezoid at (1, 4): 7
Closest shape is the yellow rectangle at (2, 3) with distance 5</think>
<answer>(2, 3)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Right triangle: } a=9, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 9 \times 3 = 13.5$
$\text{Rectangle: } w=7, h=6 \Rightarrow A=w \times h = 7 \times 6 = 42$
$\text{Rectangle: } w=5, h=6 \Rightarrow A=w \times h = 5 \times 6 = 30$
$\text{Trapezoid: } a=3, b=4, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+4}2 \times 4 = 14.0$
$\text{Right triangle: } a=5, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 5 \times 3 = 7.5$</think>
<answer>188</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=9, b=5 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 9 \times 5 = 22.5$
$\text{Trapezoid: } a=5, b=3, h=3 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+3}2 \times 3 = 12.0$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$</think>
<answer>45</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$
$\text{Rectangle: } w=5, h=8 \Rightarrow A=w \times h = 5 \times 8 = 40$
$\text{Trapezoid: } a=1, b=3, h=2 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+3}2 \times 2 = 4.0$
$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$
$\text{Square: } s=2 \Rightarrow A=s^2=2^2=4$</think>
<answer>52</answer> |
|
There are 5 shapes on a 9x9 grid. Which shape is closest to the purple square? | <think>Target shape: purple square at (7, 2)
Distance from target shape to cyan equilateral_triangle at (1, 0): 8
Distance from target shape to red rectangle at (0, 1): 8
Distance from target shape to gray right_triangle at (6, 8): 7
Distance from target shape to green square at (0, 4): 9
Closest shape is the gray right_triangle at (6, 8) with distance 7</think>
<answer>(6, 8)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=8, b=8 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 8 = 32.0$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$
$\text{Equilateral triangle: } s=1 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 1^2 = 0.43$</think>
<answer>48</answer> |
|
There are 5 shapes on a 9x9 grid. Which shape is closest to the cyan trapezoid? | <think>Target shape: cyan trapezoid at (3, 4)
Distance from target shape to gray rectangle at (1, 5): 3
Distance from target shape to orange equilateral_triangle at (0, 1): 6
Distance from target shape to blue square at (2, 8): 5
Distance from target shape to green trapezoid at (0, 3): 4
Closest shape is the gray rectangle at (1, 5) with distance 3</think>
<answer>(1, 5)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Trapezoid: } a=1, b=6, h=5 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+6}2 \times 5 = 17.5$
$\text{Right triangle: } a=9, b=8 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 9 \times 8 = 36.0$
$\text{Square: } s=4 \Rightarrow A=s^2=4^2=16$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$
$\text{Trapezoid: } a=6, b=6, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{6+6}2 \times 6 = 36.0$</think>
<answer>188</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=4, b=4 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 4 = 8.0$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$
$\text{Equilateral triangle: } s=8 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 8^2 = 27.71$
$\text{Trapezoid: } a=1, b=4, h=9 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+4}2 \times 9 = 22.5$
$\text{Equilateral triangle: } s=3 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 3^2 = 3.9$</think>
<answer>78</answer> |
|
There are 4 shapes on a 10x10 grid. Which shape is closest to the red trapezoid? | <think>Target shape: red trapezoid at (8, 2)
Distance from target shape to purple right_triangle at (4, 0): 6
Distance from target shape to green right_triangle at (6, 9): 9
Distance from target shape to gray right_triangle at (9, 1): 2
Closest shape is the gray right_triangle at (9, 1) with distance 2</think>
<answer>(9, 1)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=6 \Rightarrow A=s^2=6^2=36$
$\text{Trapezoid: } a=7, b=8, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{7+8}2 \times 8 = 60.0$
$\text{Square: } s=6 \Rightarrow A=s^2=6^2=36$
$\text{Rectangle: } w=9, h=3 \Rightarrow A=w \times h = 9 \times 3 = 27$</think>
<answer>159</answer> |
|
There are 2 shapes on a 10x10 grid. Which shape is closest to the orange square? | <think>Target shape: orange square at (5, 1)
Distance from target shape to brown rectangle at (0, 6): 10
Closest shape is the brown rectangle at (0, 6) with distance 10</think>
<answer>(0, 6)</answer> |
|
There are 5 shapes on a 6x6 grid. Which shape is closest to the cyan trapezoid? | <think>Target shape: cyan trapezoid at (0, 2)
Distance from target shape to purple equilateral_triangle at (1, 4): 3
Distance from target shape to blue right_triangle at (4, 0): 6
Distance from target shape to red trapezoid at (3, 0): 5
Distance from target shape to green trapezoid at (0, 4): 2
Closest shape is the green trapezoid at (0, 4) with distance 2</think>
<answer>(0, 4)</answer> |
|
There are 7 shapes on a 3x3 grid. Which shape is closest to the cyan trapezoid? | <think>Target shape: cyan trapezoid at (0, 2)
Distance from target shape to red rectangle at (1, 1): 2
Distance from target shape to orange square at (2, 2): 2
Distance from target shape to gray square at (0, 1): 1
Distance from target shape to purple rectangle at (1, 2): 1
Distance from target shape to blue right_triangle at (2, 0): 4
Distance from target shape to pink trapezoid at (1, 0): 3
Closest shape is the gray square at (0, 1) with distance 1</think>
<answer>(0, 1)</answer> |
|
There are 6 shapes on a 8x8 grid. Which shape is closest to the gray right_triangle? | <think>Target shape: gray right_triangle at (7, 2)
Distance from target shape to red right_triangle at (3, 7): 9
Distance from target shape to brown rectangle at (5, 1): 3
Distance from target shape to orange square at (7, 3): 1
Distance from target shape to purple equilateral_triangle at (6, 5): 4
Distance from target shape to pink trapezoid at (0, 1): 8
Closest shape is the orange square at (7, 3) with distance 1</think>
<answer>(7, 3)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$
$\text{Equilateral triangle: } s=1 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 1^2 = 0.43$
$\text{Trapezoid: } a=8, b=3, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{8+3}2 \times 6 = 33.0$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$</think>
<answer>46</answer> |
|
There are 7 shapes on a 10x10 grid. Which shape is closest to the orange trapezoid? | <think>Target shape: orange trapezoid at (0, 4)
Distance from target shape to gray equilateral_triangle at (8, 9): 13
Distance from target shape to brown equilateral_triangle at (5, 9): 10
Distance from target shape to green right_triangle at (8, 5): 9
Distance from target shape to purple right_triangle at (1, 1): 4
Distance from target shape to cyan equilateral_triangle at (0, 5): 1
Distance from target shape to pink equilateral_triangle at (9, 8): 13
Closest shape is the cyan equilateral_triangle at (0, 5) with distance 1</think>
<answer>(0, 5)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=9 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 9^2 = 35.07$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$
$\text{Square: } s=5 \Rightarrow A=s^2=5^2=25$</think>
<answer>71</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=5, b=7, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+7}2 \times 7 = 42.0$
$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$</think>
<answer>45</answer> |
|
There are 5 shapes on a 3x3 grid. Which shape is closest to the pink equilateral_triangle? | <think>Target shape: pink equilateral_triangle at (1, 1)
Distance from target shape to orange square at (1, 0): 1
Distance from target shape to blue rectangle at (2, 0): 2
Distance from target shape to brown trapezoid at (2, 1): 1
Distance from target shape to yellow rectangle at (0, 1): 1
Closest shape is the orange square at (1, 0) with distance 1</think>
<answer>(1, 0)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=4, b=9, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{4+9}2 \times 4 = 26.0$
$\text{Trapezoid: } a=5, b=8, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+8}2 \times 7 = 45.5$
$\text{Right triangle: } a=5, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 5 \times 1 = 2.5$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$
$\text{Trapezoid: } a=3, b=9, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+9}2 \times 4 = 24.0$
$\text{Equilateral triangle: } s=1 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 1^2 = 0.43$
$\text{Trapezoid: } a=7, b=1, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{7+1}2 \times 7 = 28.0$</think>
<answer>142</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=5, b=7, h=1 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+7}2 \times 1 = 6.0$
$\text{Right triangle: } a=4, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 1 = 2.0$
$\text{Trapezoid: } a=7, b=4, h=9 \Rightarrow A=\frac{a+b}2 \times h = \frac{7+4}2 \times 9 = 49.5$
$\text{Right triangle: } a=4, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 9 = 18.0$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$</think>
<answer>86</answer> |
|
There are 2 shapes on a 7x7 grid. Which shape is closest to the green square? | <think>Target shape: green square at (3, 2)
Distance from target shape to blue equilateral_triangle at (4, 0): 3
Closest shape is the blue equilateral_triangle at (4, 0) with distance 3</think>
<answer>(4, 0)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=6, b=1, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{6+1}2 \times 8 = 28.0$
$\text{Right triangle: } a=4, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 1 = 2.0$</think>
<answer>30</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=8, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 9 = 36.0$
$\text{Rectangle: } w=4, h=8 \Rightarrow A=w \times h = 4 \times 8 = 32$
$\text{Right triangle: } a=1, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 3 = 1.5$
$\text{Equilateral triangle: } s=7 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 7^2 = 21.22$
$\text{Rectangle: } w=2, h=4 \Rightarrow A=w \times h = 2 \times 4 = 8$
$\text{Trapezoid: } a=9, b=4, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{9+4}2 \times 6 = 39.0$
$\text{Right triangle: } a=1, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 9 = 4.5$
$\text{Rectangle: } w=5, h=2 \Rightarrow A=w \times h = 5 \times 2 = 10$</think>
<answer>152</answer> |
|
There are 2 shapes on a 7x7 grid. Which shape is closest to the blue trapezoid? | <think>Target shape: blue trapezoid at (3, 4)
Distance from target shape to pink right_triangle at (6, 4): 3
Closest shape is the pink right_triangle at (6, 4) with distance 3</think>
<answer>(6, 4)</answer> |
|
There are 7 shapes on a 4x4 grid. Which shape is closest to the pink square? | <think>Target shape: pink square at (2, 1)
Distance from target shape to blue equilateral_triangle at (0, 3): 4
Distance from target shape to red square at (1, 1): 1
Distance from target shape to green rectangle at (1, 2): 2
Distance from target shape to brown trapezoid at (0, 0): 3
Distance from target shape to purple equilateral_triangle at (2, 3): 2
Distance from target shape to yellow square at (1, 3): 3
Closest shape is the red square at (1, 1) with distance 1</think>
<answer>(1, 1)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=5, b=4, h=3 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+4}2 \times 3 = 13.5$
$\text{Square: } s=7 \Rightarrow A=s^2=7^2=49$
$\text{Trapezoid: } a=3, b=7, h=9 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+7}2 \times 9 = 45.0$
$\text{Right triangle: } a=8, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 3 = 12.0$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$
$\text{Trapezoid: } a=1, b=4, h=9 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+4}2 \times 9 = 22.5$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$</think>
<answer>173</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=3, b=8, h=4 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+8}2 \times 4 = 22.0$
$\text{Right triangle: } a=7, b=8 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 7 \times 8 = 28.0$
$\text{Rectangle: } w=6, h=4 \Rightarrow A=w \times h = 6 \times 4 = 24$
$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Trapezoid: } a=1, b=5, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{1+5}2 \times 6 = 18.0$
$\text{Right triangle: } a=1, b=6 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 6 = 3.0$</think>
<answer>176</answer> |
|
There are 6 shapes on a 10x10 grid. Which shape is closest to the green trapezoid? | <think>Target shape: green trapezoid at (0, 1)
Distance from target shape to blue rectangle at (5, 2): 6
Distance from target shape to red right_triangle at (9, 6): 14
Distance from target shape to gray right_triangle at (3, 9): 11
Distance from target shape to cyan right_triangle at (9, 8): 16
Distance from target shape to brown rectangle at (2, 6): 7
Closest shape is the blue rectangle at (5, 2) with distance 6</think>
<answer>(5, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=9, b=3, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{9+3}2 \times 6 = 36.0$
$\text{Rectangle: } w=1, h=4 \Rightarrow A=w \times h = 1 \times 4 = 4$
$\text{Trapezoid: } a=6, b=6, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{6+6}2 \times 7 = 42.0$
$\text{Equilateral triangle: } s=1 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 1^2 = 0.43$
$\text{Right triangle: } a=8, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 8 \times 3 = 12.0$
$\text{Equilateral triangle: } s=4 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 4^2 = 6.93$
$\text{Rectangle: } w=9, h=8 \Rightarrow A=w \times h = 9 \times 8 = 72$
$\text{Trapezoid: } a=5, b=5, h=2 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+5}2 \times 2 = 10.0$</think>
<answer>183</answer> |
|
There are 2 shapes on a 4x4 grid. Which shape is closest to the yellow equilateral_triangle? | <think>Target shape: yellow equilateral_triangle at (1, 1)
Distance from target shape to orange square at (1, 3): 2
Closest shape is the orange square at (1, 3) with distance 2</think>
<answer>(1, 3)</answer> |
|
There are 4 shapes on a 4x4 grid. Which shape is closest to the cyan right_triangle? | <think>Target shape: cyan right_triangle at (1, 3)
Distance from target shape to gray rectangle at (3, 2): 3
Distance from target shape to pink rectangle at (1, 2): 1
Distance from target shape to brown equilateral_triangle at (1, 1): 2
Closest shape is the pink rectangle at (1, 2) with distance 1</think>
<answer>(1, 2)</answer> |
|
There are 4 shapes on a 7x7 grid. Which shape is closest to the red rectangle? | <think>Target shape: red rectangle at (4, 4)
Distance from target shape to brown square at (1, 3): 4
Distance from target shape to orange equilateral_triangle at (3, 5): 2
Distance from target shape to purple right_triangle at (2, 2): 4
Closest shape is the orange equilateral_triangle at (3, 5) with distance 2</think>
<answer>(3, 5)</answer> |
|
There are 8 shapes on a 3x3 grid. Which shape is closest to the red square? | <think>Target shape: red square at (2, 2)
Distance from target shape to green right_triangle at (0, 2): 2
Distance from target shape to blue equilateral_triangle at (2, 0): 2
Distance from target shape to cyan equilateral_triangle at (1, 0): 3
Distance from target shape to pink equilateral_triangle at (0, 0): 4
Distance from target shape to brown trapezoid at (1, 2): 1
Distance from target shape to gray equilateral_triangle at (0, 1): 3
Distance from target shape to purple trapezoid at (2, 1): 1
Closest shape is the brown trapezoid at (1, 2) with distance 1</think>
<answer>(1, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=4 \Rightarrow A=s^2=4^2=16$
$\text{Trapezoid: } a=5, b=6, h=1 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+6}2 \times 1 = 5.5$
$\text{Square: } s=4 \Rightarrow A=s^2=4^2=16$
$\text{Rectangle: } w=6, h=7 \Rightarrow A=w \times h = 6 \times 7 = 42$
$\text{Square: } s=1 \Rightarrow A=s^2=1^2=1$
$\text{Trapezoid: } a=3, b=8, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+8}2 \times 7 = 38.5$
$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Rectangle: } w=8, h=8 \Rightarrow A=w \times h = 8 \times 8 = 64$</think>
<answer>264</answer> |
|
There are 4 shapes on a 10x10 grid. Which shape is closest to the brown square? | <think>Target shape: brown square at (8, 1)
Distance from target shape to red trapezoid at (3, 0): 6
Distance from target shape to orange trapezoid at (0, 4): 11
Distance from target shape to pink trapezoid at (6, 0): 3
Closest shape is the pink trapezoid at (6, 0) with distance 3</think>
<answer>(6, 0)</answer> |
|
There are 7 shapes on a 4x4 grid. Which shape is closest to the green equilateral_triangle? | <think>Target shape: green equilateral_triangle at (0, 2)
Distance from target shape to orange rectangle at (0, 1): 1
Distance from target shape to red right_triangle at (3, 0): 5
Distance from target shape to blue right_triangle at (1, 2): 1
Distance from target shape to brown equilateral_triangle at (2, 0): 4
Distance from target shape to gray square at (1, 0): 3
Distance from target shape to purple rectangle at (3, 2): 3
Closest shape is the orange rectangle at (0, 1) with distance 1</think>
<answer>(0, 1)</answer> |
|
There are 8 shapes on a 5x5 grid. Which shape is closest to the green rectangle? | <think>Target shape: green rectangle at (3, 3)
Distance from target shape to brown equilateral_triangle at (2, 0): 4
Distance from target shape to blue trapezoid at (1, 3): 2
Distance from target shape to pink square at (3, 4): 1
Distance from target shape to yellow square at (3, 2): 1
Distance from target shape to cyan trapezoid at (2, 1): 3
Distance from target shape to purple right_triangle at (4, 0): 4
Distance from target shape to gray right_triangle at (2, 4): 2
Closest shape is the pink square at (3, 4) with distance 1</think>
<answer>(3, 4)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=2, b=4, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{2+4}2 \times 6 = 18.0$
$\text{Rectangle: } w=8, h=2 \Rightarrow A=w \times h = 8 \times 2 = 16$
$\text{Trapezoid: } a=9, b=2, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{9+2}2 \times 7 = 38.5$</think>
<answer>72</answer> |
|
There are 3 shapes on a 7x7 grid. Which shape is closest to the yellow right_triangle? | <think>Target shape: yellow right_triangle at (1, 4)
Distance from target shape to purple equilateral_triangle at (0, 2): 3
Distance from target shape to pink square at (4, 0): 7
Closest shape is the purple equilateral_triangle at (0, 2) with distance 3</think>
<answer>(0, 2)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=6, b=6, h=1 \Rightarrow A=\frac{a+b}2 \times h = \frac{6+6}2 \times 1 = 6.0$
$\text{Rectangle: } w=1, h=8 \Rightarrow A=w \times h = 1 \times 8 = 8$</think>
<answer>14</answer> |
|
There are 3 shapes on a 10x10 grid. Which shape is closest to the brown rectangle? | <think>Target shape: brown rectangle at (5, 9)
Distance from target shape to orange equilateral_triangle at (8, 8): 4
Distance from target shape to yellow trapezoid at (0, 2): 12
Closest shape is the orange equilateral_triangle at (8, 8) with distance 4</think>
<answer>(8, 8)</answer> |
|
There are 6 shapes on a 7x7 grid. Which shape is closest to the gray equilateral_triangle? | <think>Target shape: gray equilateral_triangle at (5, 3)
Distance from target shape to purple right_triangle at (3, 6): 5
Distance from target shape to yellow right_triangle at (2, 3): 3
Distance from target shape to brown equilateral_triangle at (1, 0): 7
Distance from target shape to orange square at (3, 0): 5
Distance from target shape to cyan right_triangle at (3, 3): 2
Closest shape is the cyan right_triangle at (3, 3) with distance 2</think>
<answer>(3, 3)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Trapezoid: } a=8, b=6, h=5 \Rightarrow A=\frac{a+b}2 \times h = \frac{8+6}2 \times 5 = 35.0$
$\text{Trapezoid: } a=5, b=3, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{5+3}2 \times 8 = 32.0$
$\text{Rectangle: } w=9, h=1 \Rightarrow A=w \times h = 9 \times 1 = 9$
$\text{Rectangle: } w=8, h=9 \Rightarrow A=w \times h = 8 \times 9 = 72$
$\text{Equilateral triangle: } s=6 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 6^2 = 15.59$</think>
<answer>164</answer> |
|
There are 4 shapes on a 7x7 grid. Which shape is closest to the blue equilateral_triangle? | <think>Target shape: blue equilateral_triangle at (6, 5)
Distance from target shape to yellow square at (6, 6): 1
Distance from target shape to red right_triangle at (2, 1): 8
Distance from target shape to purple equilateral_triangle at (6, 4): 1
Closest shape is the yellow square at (6, 6) with distance 1</think>
<answer>(6, 6)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=4, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 4 \times 1 = 2.0$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$
$\text{Right triangle: } a=9, b=1 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 9 \times 1 = 4.5$
$\text{Rectangle: } w=6, h=2 \Rightarrow A=w \times h = 6 \times 2 = 12$
$\text{Equilateral triangle: } s=8 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 8^2 = 27.71$
$\text{Trapezoid: } a=3, b=3, h=8 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+3}2 \times 8 = 24.0$
$\text{Rectangle: } w=6, h=3 \Rightarrow A=w \times h = 6 \times 3 = 18$
$\text{Rectangle: } w=8, h=4 \Rightarrow A=w \times h = 8 \times 4 = 32$</think>
<answer>131</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Right triangle: } a=6, b=9 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 6 \times 9 = 27.0$
$\text{Trapezoid: } a=3, b=6, h=7 \Rightarrow A=\frac{a+b}2 \times h = \frac{3+6}2 \times 7 = 31.5$</think>
<answer>58</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$
$\text{Right triangle: } a=1, b=3 \Rightarrow A=\frac{1}{2} \times a \times b = \frac{1}{2} \times 1 \times 3 = 1.5$
$\text{Equilateral triangle: } s=3 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 3^2 = 3.9$
$\text{Equilateral triangle: } s=5 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 5^2 = 10.83$
$\text{Rectangle: } w=4, h=9 \Rightarrow A=w \times h = 4 \times 9 = 36$
$\text{Square: } s=5 \Rightarrow A=s^2=5^2=25$</think>
<answer>79</answer> |
|
There are 6 shapes on a 8x8 grid. Which shape is closest to the orange square? | <think>Target shape: orange square at (7, 7)
Distance from target shape to blue equilateral_triangle at (1, 2): 11
Distance from target shape to yellow right_triangle at (1, 3): 10
Distance from target shape to red trapezoid at (0, 2): 12
Distance from target shape to green trapezoid at (5, 0): 9
Distance from target shape to cyan square at (0, 1): 13
Closest shape is the green trapezoid at (5, 0) with distance 9</think>
<answer>(5, 0)</answer> |
|
There are 2 shapes on a 9x9 grid. Which shape is closest to the pink rectangle? | <think>Target shape: pink rectangle at (1, 7)
Distance from target shape to gray equilateral_triangle at (8, 1): 13
Closest shape is the gray equilateral_triangle at (8, 1) with distance 13</think>
<answer>(8, 1)</answer> |
|
What is the total area of all shapes shown in the image, please round the result into the nearest integer? | <think>$\text{Square: } s=9 \Rightarrow A=s^2=9^2=81$
$\text{Trapezoid: } a=7, b=8, h=6 \Rightarrow A=\frac{a+b}2 \times h = \frac{7+8}2 \times 6 = 45.0$
$\text{Square: } s=6 \Rightarrow A=s^2=6^2=36$
$\text{Square: } s=4 \Rightarrow A=s^2=4^2=16$
$\text{Rectangle: } w=3, h=2 \Rightarrow A=w \times h = 3 \times 2 = 6$
$\text{Equilateral triangle: } s=2 \Rightarrow A=\frac{\sqrt{3}}4 \times s^2 = \frac{\sqrt{3}}4 \times 2^2 = 1.73$</think>
<answer>186</answer> |
|
There are 3 shapes on a 4x4 grid. Which shape is closest to the brown right_triangle? | <think>Target shape: brown right_triangle at (0, 1)
Distance from target shape to orange rectangle at (2, 3): 4
Distance from target shape to pink rectangle at (2, 1): 2
Closest shape is the pink rectangle at (2, 1) with distance 2</think>
<answer>(2, 1)</answer> |
|
There are 5 shapes on a 6x6 grid. Which shape is closest to the brown square? | <think>Target shape: brown square at (4, 3)
Distance from target shape to purple rectangle at (5, 3): 1
Distance from target shape to yellow square at (5, 4): 2
Distance from target shape to cyan square at (2, 4): 3
Distance from target shape to green rectangle at (4, 4): 1
Closest shape is the purple rectangle at (5, 3) with distance 1</think>
<answer>(5, 3)</answer> |
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 40