Yuting6/geoqa-r1v-8k-rotated huggingface dataset:
Problem: <image>Question: Let $a$ and $b$ be the lengths of the two shorter sides of the right-angled triangle shown in the diagram. The longest side, $D$, is the diameter of the large circle and $d$ is the diameter of the small circle, which touches all three sides of the triangle.
Which one of the following expressions is equal to $D+d$ ? <image1>
Choices:
A. $(a+b)$
B. $2(a+b)$
C. $\frac{1}{2}(a+b)$
D. $\sqrt{a b}$
E. $\sqrt{a^{2}+b^{2}}$
Answer: A
Problem: <image>Question: Which of the following is a net for the cube with two holes shown alongside?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: The solid shown on the right is made from two cubes. The small cube with edges $1 \mathrm{~cm}$ long sits on top of a bigger cube with edges $3 \mathrm{~cm}$ long. What is the surface area of the whole solid? <image1>
Choices:
A. $56 \mathrm{~cm}^{2}$
B. $58 \mathrm{~cm}^{2}$
C. $60 \mathrm{~cm}^{2}$
D. $62 \mathrm{~cm}^{2}$
E. $64 \mathrm{~cm}^{2}$
Answer: B
Problem: <image>Question: If all the statements in the box are true, which of $\mathrm{A}, \mathrm{B}, \mathrm{C}$, $\mathrm{D}$ or $\mathrm{E}$ can be deduced? <image1>
Choices:
A. It's red
B. It's a blue square
C. It's red and round
D. It's yellow and round
E. It's blue and round
Answer: E
Problem: <image>Question: The rectangle shown in the diagram on the right is divided into 7 squares. The sides of the grey squares on the right are all $8 \mathrm{~cm}$ long. What is the length in $\mathrm{cm}$ of the side of the black square? <image1>
Answer: 18
Problem: <image>Question: Max and Moritz have drawn out a $5 \times 5$ grid on the playground, together with three obstacles. They want to walk from $P$ to $Q$ using the shortest route, avoiding the obstacles and always crossing a common edge to go from the centre of one square to the centre of the next. How many such shortest paths are there from $P$ to $Q$ ? <image1>
Answer: 12
Problem: <image>Question: Belinda is making patterns using identical matchsticks. The $1 \times 1,2 \times 2$ and $3 \times 3$ patterns are shown on the right. How many matchsticks should Belinda add to the $30 \times 30$ pattern in order to make the $31 \times 31$ pattern? <image1>
Answer: 124
Problem: <image>Question: The regular pentagon $P Q R S T$ in the diagram has been reflected in the line $P Q$ so that vertex $T$ is reflected to point $U$, as shown. Then the new pentagon is reflected in $P U$, so that vertex $Q$ is reflected to point $V$, as shown. This process is repeated, on each occasion reflecting in the line determined by the new edge through $P$.
What is the least number of such reflections that are needed to return pentagon $P Q R S T$ to its original position?
<image1>
Answer: 10
Problem: <image>Question: <image1>
In the diagram above there are 11 cards, each printed with two letters. The diagram below shows a rearangement of the cards, but only the top letters are shown.
<image2>
Which one of the following sequences of letters could appear on the bottom row of the second diagram?
Choices:
A. ANJAMKILIOR
B. RLIIMKOJNAA
C. JANAMKILIRO
D. RAONJMILIKA
E. ANMAIKOLIRJ
Answer: E
Problem: <image>Question: The robot in the diagram has been programmed to move in a straight line and, if it meets a wall (shown by bold lines), to turn right by $90^{\circ}$ and then to continue straight on. If it cannot go straight or turn right it will stop. What will happen to this robot? <image1>
Choices:
A. It will stop at $\mathrm{P} 2$.
B. It will stop at P1.
C. It will stop at $\mathrm{T} 1$.
D. It will stop at $S 1$.
E. It will never stop.
Answer: E
Problem: <image>Question: What is the least possible number of small squares that we should shade in the diagram on the right for the whole diagram to have a line of symmetry? <image1>
Answer: 3
Problem: <image>Question: In the diagram six circles of equal size touch adjacent circles and the sides of the large rectangle. Each of the corners of the small rectangle is the centre of one of the circles. The perimeter of the small rectangle is $60 \mathrm{~cm}$. What is the perimeter of the large rectangle in centimetres? <image1>
Answer: 100
Problem: <image>Question: In the diagram, each of the squares touches adjacent squares at its corners and the line $G H$ along one of its edges. The line $G H$ is $24 \mathrm{~cm}$ long. What is the total perimeter, in centimetres, of all the squares? <image1>
Answer: 96
Problem: <image>Question: By drawing 9 lines, 5 horizontal and 4 vertical, one can form 12 small rectangles, as shown on the right. What is the greatest possible number of small rectangles one can form by drawing 15 lines, either horizontal or vertical? <image1>
Answer: 42
Problem: <image>Question: In the diagram, $V W X$ and $X Y Z$ are congruent equilateral triangles and angle $V X Y=80^{\circ}$. What is the size of angle $V W Y$ ? <image1>
Choices:
A. $25^{\circ}$
B. $30^{\circ}$
C. $35^{\circ}$
D. $40^{\circ}$
E. $45^{\circ}$
Answer: D
Problem: <image>Question: Each object shown is made up of 7 cubes. Which of $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ can be obtained by rotating $\mathrm{T}$ ?
<image1>
Choices:
A. P and R
B. Q and S
C. only R
D. none of them
E. P, Q and R
Answer: A
Problem: <image>Question: The diagram shows a square of side $2 \mathrm{~m}$ with lines drawn to its sides from the centre $O$. The points $A, B, C$ and $D$ are all on different sides of the square. The lines $O A$ and $O B$ are perpendicular as are the lines $O C$ and $O D$. What is the shaded area in square metres? <image1>
Answer: 2
Problem: <image>Question: Nick and Pete each chose four numbers from the nine numbers in the diagram on the right. There was one number which neither of them chose. Nick found that the total of his numbers was three times Pete's total. Which number was not chosen? <image1>
Answer: 14
Problem: <image>Question: Marta wants to use 16 square tiles like the one shown to form a $4 \times 4$ square design. The tiles may be turned. Each arc bisects the sides it meets and has length $p \mathrm{~cm}$. She is trying to make the arcs connect to make a long path. What is the length, in centimetres, of the longest possible path? <image1>
Choices:
A. $15 p$
B. $20 p$
C. $21 p$
D. $22 p$
E. $25 p$
Answer: D
Problem: <image>Question: In the diagram, a square with sides of length $4 \mathrm{~cm}$ and a triangle with the same perimeter as the square are joined together to form a pentagon. What is the perimeter of the pentagon? <image1>
Choices:
A. $12 \mathrm{~cm}$
B. $24 \mathrm{~cm}$
C. $28 \mathrm{~cm}$
D. $32 \mathrm{~cm}$
E. It depends on the size of the triangle
Answer: B
Problem: <image>Question: How many different squares can be drawn in total by joining the dots with line segments in the part of the square lattice as shown on the right? <image1>
Answer: 4
Problem: <image>Question: In the diagram, three lines intersect at one point, forming angles of $108^{\circ}$ and $124^{\circ}$, as shown. What is the size of the angle marked $x^{\circ}$ ? <image1>
Choices:
A. $56^{\circ}$
B. $55^{\circ}$
C. $54^{\circ}$
D. $53^{\circ}$
E. $52^{\circ}$
Answer: E
Problem: <image>Question: A shape is made by cutting all the corners off a cube, as shown in the diagram. How many edges does the shape have? <image1>
Answer: 36
Problem: <image>Question: Four tangent circles, each of radius $6 \mathrm{~cm}$, are inscribed in a rectangle $P Q R S$ as shown in the diagram. The sides of the rectangle touch two of the circles at $T$ and $U$. What is the area of triangle RUT in $\mathrm{cm}^{2}$ ? <image1>
Answer: 108
Problem: <image>Question: In the subtraction calculation on the right, each of the letters $\mathrm{K}, \mathrm{A}, \mathrm{N}, \mathrm{G}, \mathrm{R}$ and $\mathrm{O}$ represents a different digit.
What is the largest possible value of the number 'KAN'?
<image1>
Answer: 864
Problem: <image>Question: Four identical dice are arranged in a row as shown in the diagram. Although each die does have 1, 2, 3, 4, 5, 6 dots, the sum of the numbers of dots on each pair of opposite faces is not necessarily 7 . What is the total number of dots on the six touching faces of the dice?
<image1>
Answer: 20
Problem: <image>Question: The star on the right is formed from 12 identical equilateral triangles. The length of the perimeter of the star is $36 \mathrm{~cm}$. What is the length of the perimeter of the shaded hexagon? <image1>
Choices:
A. $12 \mathrm{~cm}$
B. $18 \mathrm{~cm}$
C. $24 \mathrm{~cm}$
D. $30 \mathrm{~cm}$
E. $36 \mathrm{~cm}$
Answer: B
Problem: <image>Question: In the diagram on the right, $Q S R$ is a straight line, $\angle Q P S=12^{\circ}$ and $P Q=P S=R S$.
What is the size of $\angle Q P R$ ? <image1>
Choices:
A. $36^{\circ}$
B. $42^{\circ}$
C. $54^{\circ}$
D. $60^{\circ}$
E. $84^{\circ}$
Answer: C
Problem: <image>Question: Which of the following knots consist of more than one loop of rope?
<image1>
Choices:
A. $P, R$ and $T$
B. $R, S$ and $T$
C. $P, R, S$ and $T$
D. $$ all of $P, Q, R, S$ and $T$
E. $$ none of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ or $\mathrm{D}$
Answer: A
Problem: <image>Question: The diagram on the right shows nine points in a square array. What is the smallest number of points that need to be removed in order that no three of the remaining points are in a straight line? <image1>
Answer: 3
Problem: <image>Question: The diagram shows four circles each of which touches the largest square and two adjacent circles. A second square has its vertices at the midpoints of the sides of the largest square and the central square has its vertices at the centres of the circles.
<image1>
What is the ratio of the total shaded area to the area of the outer square?
Choices:
A. $\pi: 12$
B. $1: 4$
C. $(\pi+2): 16$
D. $1: 3$
E. $\pi: 4$
Answer: B
Problem: <image>Question: The diagram shows a solid with six triangular faces. At each vertex there is a number and two of the numbers are 1 and 5, as shown. For each face the sum of the numbers at the three vertices of each face is calculated, and all the sums are the same. What is the sum of all five numbers at the vertices? <image1>
Answer: 17
Problem: <image>Question: In each of the squares in the grid, one of the letters $P, Q, R$ and $S$ must be entered in such a way that adjacent squares (whether connected by an edge or just a corner) do not contain the same letter. Some of the letters have already been entered as shown.
What are the possibilities for the letter in the shaded square?
<image1>
Choices:
A. only $Q$
B. only $R$
C. only $S$
D. either $R$ or $S$, but no others
E. it is impossible to complete the grid
Answer: D
Problem: <image>Question: The diagram shows a regular 9-sided polygon (a nonagon or an enneagon) with two of the sides extended to meet at the point $X$. What is the size of the acute angle at $X$ ? <image1>
Choices:
A. $40^{\circ}$
B. $45^{\circ}$
C. $50^{\circ}$
D. $55^{\circ}$
E. $60^{\circ}$
Answer: E
Problem: <image>Question: The diagram shows the first three patterns in a sequence in which each pattern has a square hole in the middle. How many small shaded squares are needed to build the tenth pattern in the sequence?
<image1>
Answer: 92
Problem: <image>Question: An ant crawls carefully around the edges of a cube, starting at point $P$ and in the direction of the arrow. At the end of the first edge he chooses to go either left or right. He then turns the other way at the end of the next edge and continues like this, turning right or left alternately at the end of each successive edge. After how many edges does the ant return to point $P$ for the first time? <image1>
Answer: 6
Problem: <image>Question: The fractions $\frac{1}{3}$ and $\frac{1}{5}$ have been placed on the
<image1>
number-line shown on the right. At which position should the fraction $\frac{1}{4}$ be placed?
Choices:
A. $a$
B. $b$
C. $C$
D. $d$
E. $e$
Answer: A
Problem: <image>Question: Three cuts are made through a large cube to make eight smaller cuboids, as shown in the diagram on the right. What is the ratio of the total surface area of these eight cuboids to the total surface area of the original cube?
<image1>
Choices:
A. $1: 1$
B. $4: 3$
C. $3: 2$
D. $2: 1$
E. $4: 1$
Answer: D
Problem: <image>Question: The diagram shows the plan of a room. Adjoining walls are perpendicular to each other and the lengths of some of the walls are shown. What is the length of the perimeter of the room? <image1>
Choices:
A. $3 a+4 b$
B. $3 a+8 b$
C. $6 a+4 b$
D. $6 a+6 b$
E. $6 a+8 b$
Answer: E
Problem: <image>Question: The diagram (which is not drawn to scale) shows a box measuring $5 \mathrm{~cm}$ by $5 \mathrm{~cm}$. There are seven bars in the box, each measuring $1 \mathrm{~cm}$ by $3 \mathrm{~cm}$. Kanga wants to slide the bars in the box so there is room for one more bar. What is the minimum number of bars that Kanga needs to move?

<image1>
Answer: 3
Problem: <image>Question: A large square is divided into 4 equal-sized smaller squares. All the smaller squares are either shaded or unshaded. How many different ways are there to colour the large square? (Two colourings are considered to be the same if one can be rotated to look exactly like the other, as in the example shown.)
<image1>
Answer: 6
Problem: <image>Question: The diagram shows a quadrilateral $A B C D$, in which $A D=B C$, $\angle C A D=50^{\circ}, \angle A C D=65^{\circ}$ and $\angle A C B=70^{\circ}$.
<image1>
What is the size of $\angle A B C$ ?
Choices:
A. $50^{\circ}$
B. $55^{\circ}$
C. $60^{\circ}$
D. $65^{\circ}$
E. Impossible to determine
Answer: B
Problem: <image>Question: Andrea has wound some rope around a piece of wood, as shown in the diagram on the right. She rotates the wood $180^{\circ}$ as shown by the arrow in the diagram. What does she see after the rotation?
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: The diagram (which is not drawn to scale) shows a rectangle $A B C D$ and a square $P Q R S$, in which $P Q=B C=6 \mathrm{~cm}$ and $C D=10 \mathrm{~cm} . P Q$ is parallel to $A B$. The shaded area is half the area of $A B C D$.
<image1>
What is the length, in $\mathrm{cm}$, of $P X$ ?
Answer: 1
Problem: <image>Question: The diagram shows a logo made entirely from semicircular arcs, each with a radius of $2 \mathrm{~cm}, 4 \mathrm{~cm}$ or $8 \mathrm{~cm}$. What fraction of the logo is shaded? <image1>
Choices:
A. $\frac{1}{3}$
B. $\frac{1}{4}$
C. $\frac{1}{5}$
D. $\frac{2}{3}$
E. $\frac{3}{4}$
Answer: B
Problem: <image>Question: In the figure there are nine regions inside the five circles. All of the numbers from 1 to 9 are written in the regions, one to each region, so that the sum of the numbers inside each circle is 11 .
Which number must be written in the region with the question mark?
<image1>
Answer: 5
Problem: <image>Question: Mr Gagac goes to a barter market where the items are exchanged according to the table on the right. Mr Gagac wants to take away 1 goose, 1 turkey and 1 duck. What is the minimum number of hens that he needs to bring to the barter market?
<image1>
Answer: 16
Problem: <image>Question: The diagram shows a large equilateral triangle divided into 36 small equilateral triangles, each with area $1 \mathrm{~cm}^{2}$. What is the area of the shaded triangle, in $\mathrm{cm}^{2}$ ? <image1>
Answer: 11
Problem: <image>Question: The diagram on the right shows an L-shape made from four small squares. Ria wants to add an extra small square in order to form a shape with a line of symmetry. In how many different ways can she do this? <image1>
Answer: 3
Problem: <image>Question: The diagram shows three squares. The medium square is formed by joining the midpoints of the sides of the large square. The small square is formed by joining the midpoints of the sides of the medium square. The area of the small square is $6 \mathrm{~cm}^{2}$. What is the difference between the area of the medium square and the area of the large square? <image1>
Choices:
A. $3 \mathrm{~cm}^{2}$
B. $6 \mathrm{~cm}^{2}$
C. $9 \mathrm{~cm}^{2}$
D. $12 \mathrm{~cm}^{2}$
E. $15 \mathrm{~cm}^{2}$
Answer: D
Problem: <image>Question: Each region in the figure is to be coloured with one of four colours: red $(\mathrm{R})$, green $(\mathrm{G})$, orange $(\mathrm{O})$ or yellow $(\mathrm{Y})$. The colours of only three regions are shown. Any two regions that touch must have different colours. <image1> The colour of the region $\mathrm{X}$ is:
Choices:
A. red
B. orange
C. green
D. yellow
E. impossible to determine
Answer: A
Problem: <image>Question: A square piece of paper is cut into six rectangular pieces as shown in the diagram. When the lengths of the perimeters of the six rectangular pieces are added together, the result is $120 \mathrm{~cm}$. What is the area of the square piece of paper? <image1>
Choices:
A. $48 \mathrm{~cm}^{2}$
B. $64 \mathrm{~cm}^{2}$
C. $110.25 \mathrm{~cm}^{2}$
D. $144 \mathrm{~cm}^{2}$
E. $256 \mathrm{~cm}^{2}$
Answer: D
Problem: <image>Question: Lina has placed two shapes on a $5 \times 5$ board, as shown in the picture on the right. Which of the following five shapes should she place on the empty part of the board so that none of the remaining four shapes will fit in the empty space that is left? (The shapes may be rotated or turned over, but can only be placed so that they cover complete squares.)
<image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: The diagram on the right shows a square with side $3 \mathrm{~cm}$ inside a square with side $7 \mathrm{~cm}$ and another square with side $5 \mathrm{~cm}$ which intersects the first two squares. What is the difference between the area of the black region and the total area of the grey regions? <image1>
Choices:
A. $0 \mathrm{~cm}^{2}$
B. $10 \mathrm{~cm}^{2}$
C. $11 \mathrm{~cm}^{2}$
D. $15 \mathrm{~cm}^{2}$
E. more information needed
Answer: D
Problem: <image>Question: The first diagram on the right shows a shape constructed from two rectangles. The lengths of two sides are marked: 11 and 13. The shape is cut into three parts and the parts are rearranged, as shown in the second diagram on the right. What is the length marked $x$ ?
<image1>
Answer: 37
Problem: <image>Question: Each of the nine paths in a park is $100 \mathrm{~m}$ long. Ann wants to go from $X$ to $Y$ without going along any path more than once. What is the length of the longest route she can choose? <image1>
Choices:
A. $900 \mathrm{~m}$
B. $800 \mathrm{~m}$
C. $700 \mathrm{~m}$
D. $600 \mathrm{~m}$
E. $500 \mathrm{~m}$
Answer: C
Problem: <image>Question: The diagram (which $\underline{\text { is }}$ drawn to scale) shows two triangles. In how many ways can you choose two vertices, one in each triangle, so that the straight line through the two vertices does not cross either triangle? <image1>
Answer: 4
Problem: <image>Question: Werner folds a sheet of paper as shown in the diagram and makes two straight cuts with a pair of scissors. He then opens up the paper again. Which of the following shapes cannot be the result? <image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: D
Problem: <image>Question: Mrs Gardner has beds for peas and strawberries in her rectangular garden. This year, by moving the boundary between them, she changed her rectangular pea bed to a square by lengthening one of its sides by 3 metres. As a result of this change, the area of the strawberry bed reduced by $15 \mathrm{~m}^{2}$. What was the area of the pea bed before the change? <image1>
Choices:
A. $5 \mathrm{~m}^{2}$
B. $9 \mathrm{~m}^{2}$
C. $10 \mathrm{~m}^{2}$
D. $15 \mathrm{~m}^{2}$
E. $18 \mathrm{~m}^{2}$
Answer: C
Problem: <image>Question: Barbara wants to complete the diagram below by inserting three numbers, one into each empty cell. She wants the sum of the first three numbers to be 100 , the sum of the middle three numbers to be 200 and the sum of the last three numbers to be 300 . What number should Barbara insert into the middle cell of the diagram? <image1>
Answer: 60
Problem: <image>Question: In the figure, what is the value of $x$ ? <image1>
Answer: 51
Problem: <image>Question: Three small equilateral triangles of the same size are cut from the corners of a larger equilateral triangle with sides $6 \mathrm{~cm}$ as shown. The sum of the perimeters of the three small triangles is equal to the perimeter of the remaining hexagon. What is the side-length of one of the small triangles? <image1>
Choices:
A. $1 \mathrm{~cm}$
B. $1.2 \mathrm{~cm}$
C. $1.25 \mathrm{~cm}$
D. $1.5 \mathrm{~cm}$
E. $2 \mathrm{~cm}$
Answer: D
Problem: <image>Question: A cube is being rolled on a plane so it turns around its edges. Its bottom face passes through the positions $1,2,3,4,5,6$ and 7 in that order, as shown. Which of these two positions were occupied by the same face of the cube? <image1>
Choices:
A. 1 and 7
B. 1 and 6
C. 1 and 5
D. 2 and 7
E. 2 and 6
Answer: B
Problem: <image>Question: In the diagram, $W X Y Z$ is a square, $M$ is the midpoint of $W Z$ and $M N$ is perpendicular to $W Y$. What is the ratio of the area of the shaded triangle $M N Y$ to the area of the square? <image1>
Choices:
A. 1:6
B. 1:5
C. 7:36
D. 3:16
E. 7:40
Answer: D
Problem: <image>Question: A large triangle is divided into four smaller triangles and three quadrilaterals by three straight line segments. The sum of the perimeters of the three quadrilaterals is $25 \mathrm{~cm}$. The sum of the perimeters of the four triangles is $20 \mathrm{~cm}$. The perimeter of the original triangle is $19 \mathrm{~cm}$. What is the sum of the lengths of the three straight line segments?
<image1>
Choices:
A. $11 \mathrm{~cm}$
B. $12 \mathrm{~cm}$
C. $13 \mathrm{~cm}$
D. $15 \mathrm{~cm}$
E. $16 \mathrm{~cm}$
Answer: C
Problem: <image>Question: Each cell of the $3 \times 3$ grid shown has placed in it a positive number so that: in each row and each column, the product of the three numbers is equal to 1 ; and in each $2 \times 2$ square, the product of the four numbers is equal to 2 . What number should be placed in the central cell?
<image1>
Answer: 16
Problem: <image>Question: Ann has the square sheet of paper shown in the left-hand diagram. By cutting along lines of the square, she produces copies of the shape shown in the right-hand diagram. What is the smallest possible number of cells she can leave unused? <image1>
Answer: 4
Problem: <image>Question: Olivia and a friend are playing a game of 'battleships' on a $5 \times 5$ board. Olivia has already placed two ships as shown. She still has to place a $3 \times 1$ ship so that it covers exactly three cells. No two ships can have a boundary point in common. How many positions are there for her $3 \times 1$ ship? <image1>
Answer: 8
Problem: <image>Question: In the diagram, $\alpha=55^{\circ}, \beta=40^{\circ}$ and $\gamma=35^{\circ}$. What is the value of $\delta$ ? <image1>
Choices:
A. $100^{\circ}$
B. $105^{\circ}$
C. $120^{\circ}$
D. $125^{\circ}$
E. $130^{\circ}$
Answer: E
Problem: <image>Question: The edges of rectangle $P Q R S$ are parallel to the coordinate axes. $P Q R S$ lies below the $x$-axis and to the right of the $y$-axis as shown in the diagram. The coordinates of $P, Q, R$ and $S$ are all integers. For each point, we calculate the value $(y$-coordinate $) \div(x$-coordinate $)$. Which of the four points gives the least value? <image1>
Choices:
A. P
B. Q
C. R
D. S
E. It depends on the rectangle.
Answer: A
Problem: <image>Question: In the $6 \times 8$ grid shown, 24 cells are not intersected by either diagonal. When the diagonals of a $6 \times 10$ grid are drawn, how many cells are not intersected by either diagonal? <image1>
Answer: 32
Problem: <image>Question: John has made a building of unit cubes standing on a $4 \times 4$ grid. The diagram shows the number of cubes standing on each cell. When John looks horizontally at the building from behind, what does he see? <image1>
<image2>
Choices:
A. A
B. B
C. C
D. D
E. E
Answer: C
Problem: <image>Question: The diagram shows a shaded quadrilateral $P Q R S$ drawn on a grid. Each cell of the grid has sides of length $2 \mathrm{~cm}$. What is the area of quadrilateral $P Q R S$ ? <image1>
Choices:
A. $96 \mathrm{~cm}^{2}$
B. $84 \mathrm{~cm}^{2}$
C. $76 \mathrm{~cm}^{2}$
D. $88 \mathrm{~cm}^{2}$
E. $104 \mathrm{~cm}^{2}$
Answer: B