Objective 7: The student will demonstrate an understanding of two- and three-dimensional representations of geometric relationships and shapes.
8.7A The student is expected to draw three-dimensional figures from different perspectives and match drawings of top, front, and side views to figures.
1. (8.7A, 09-1, 9) 1. The drawings below show the left-side, front, and top views of a three-dimensional structure built with identical cubes.Which of the following 3-dimensional structures is best represented by these views?
A C
B D ß
/ 3. (8.7A, 08-1, 9) The drawing below shows a 3-dimensional structure built from identical cubes.
Which of the following does not represent a top, front, or right-side view of this 3-dimensional structure?
A B
C D ß
2. (8.7A, 09-1, 10) The grid below shows the top view of a 3-dimensional structure built using identical cubes. The numbers represent how many cubes are in each column.
Which of the following best represents this structure?
A C
B D ß
/ 4. (8.7A, 08-1, 10) The drawing represents the front view of a 3-dimensional object built with 16 cubes.
Which 3-dimensional view represents the same structure?
A C
B ß D
8.7A The student is expected to draw three-dimensional figures from different perspectives and match drawings of top, front, and side views to figures.
5. (8.7A, 06-48, 9) The drawing below shows a solid with hexagonal bases.Which drawing best represents the top view of this hexagonal solid?
A C ß
B D / 7. (8.7A, 06-11, 10) Which of the following shapes could not represent a top, front, or side view of a trapezoidal prism?
A A square
B A trapezoid
C A rectangle
D A triangle ß
8. (8.7A, 04-4, 9) The drawing shows a 3-dimensional solid.
Which best represents the shape of the solid when viewed from the top?
A Pentagon
B Hexagon ß
C Heptagon
D Octagon
6. (8.7A, 06-45, 10) Mr Lee designed a table that appears to be a cone with a wooden board passing through it, as shown below.
Which of the following best represents a top view of this table?
A C
B ß D
/ 9. (8.7A, 06-4, 9) The drawing below shows both the top view of a solid structure built with identical cubes as well as the number of cubes in each column of the structure.
Which 3-dimensional view best represents the same structure?
A ß C
B D
8.7B The student is expected to use geometric concepts and properties to solve problems in fields such as art and architecture.
1. (8.7B, 09-25, 9) Katy Perry designed a painting for art class, as shown in the drawing below. Her design contains 4 circles on a square canvas. Each circle has a radius of 6 inches. The circles touch the edges of the canvas and each other, as shown below.The shaded section of Katy Perry’s design will be painted black. Which is closest to the area that will be painted black?
A 124 in.² ß C 308 in.²
B 463 in.² D 116 in.² / 4. (8.7B, 08-2, 9) The dimensions on the blueprints of Beyoncé Knowles’ house are proportional to the house’s actual dimensions. The blueprints show the house’s rectangular foundation to be 5.5 inches wide by 9 inches long. If the foundation actually measures 36 feet long, what is the width in feet of the actual foundation?
Record your answer and fill in the bubbles on your answer document. Be sure to use the correct place value.
22 ß
2. (8.7B, 09-3, 10) A toy company plans to make a model of a train engine using a scale where 1 inch represents 4 feet. If the length of the actual engine is 51 feet, which of these is closest to the length of the model in inches?
A in. ß C in.
B 3 in. D 204 in. / 5. (8.7B, 08-2, 10) Abran has 42 linear feet of fencing to build a pen for four puppies. Which of the following statements best describes the pen he should build in order to provide the maximum area for these puppies?
A A circular pen with a radius of approximately 6.5 ft ß
B A rectangular pen with dimensions of 10 ft by 11ft
C A square pen with side lengths of 10.5 ft
D An equilateral triangular pen with side lengths of 14 ft
3. (8.7B, 09-49, 9) Taylor Swift made a model of her grandfather’s fishing boat using a scale where 2 inches represents 3 feet. Her grandfather’s actual boat is 28 feet long. What is the length of Taylor’s model boat?
A in.
B in. ß
C 22 in.
D 42 in. / 6. (8.7B, 09-40, 10) The diagram below shows the floor plan of an apartment with a rectangular floor. The ratio of the width of the bathroom floor to the width of the entire apartment floor is 3:7.
What is x, the width of the bathroom in inches?
A 112 in. C 144 in. ß
B 40 in. D 48 in.
8.7B The student is expected to use geometric concepts and properties to solve problems in fields such as art and architecture.
7. (8.7B, 06-8, 9) Olga plans to take a trip from her house in San Marcos, Texas, to a friend’s house in Zapata, Texas. She measured the distance between the two places on a map and found it to be 8 inches. If the scale on the map is inch represents 14 miles, which is closest to the actual distance in miles between the two places?A 112 mi. C 56 mi.
B 224 mi. ß D 44 mi. / 9. (8.7B, 04-41, 10) Near the downtown area of Houston, there is a vacant triangular plot of land with sides that measure 22 feet, 27 feet, and 17 feet. If the city council decides to plant an oak tree in the corner with the smallest angle, where should the tree be planted?
A In the corner opposite the side that is 17 feet ß
B In the corner opposite the side that is 22 feet
C In the corner opposite the side that is 27 feet
D In the center of the triangular plot
8. (8.7B, 04-30, 9) An artist made a drawing of a house with a tree next to it. The drawing is the size of the actual house and tree. The tallest point of the house is 12 feet 8 inches, and the tree is 27 feet tall. How many inches tall is the tree in the drawing?
A 8.4 in. C 23.4 in.
B 18 in. ß D 486 in. / 10. (8.7B, 04-49, 9) Ms Hill wants to carpet her rectangular living room, which measures 14 feet by 11 feet. If the carpet she wants to purchase costs $1.50 per square foot, including tax, how much will it cost to carpet her living room?
A $50
B $75
C $154
D $231ß
8.7C The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.
1. (8.7C, 06-23, 9) Look at the drawing shown below.If is a right triangle formed by the placement of 3 squares, what is the area of the shaded square?
A 135 in.²
B 24 in.²
C 66 in.² ß
D 88 in.² / 2. (8.7C, 04-33, 9) The drawing below shows 3 square parking lots that enclose a grassy area shaped like a right triangle.
If Lot A’s perimeter is 300 yards and Lot B’s perimeter is 400 yards, what is the perimeter of Lot C?
A 500 yd ß
B 700 yd
C 1400 yd
D 2000 yd
8.7C The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.
3. (8.7C, 09-11, 9) The drawing below shows three squares joined at their vertices to form a right triangle.What is the area of the shaded square?
A. 3529 ft² ß C. 6889 ft²
B. 1079 ft² D. 169 ft² / 5. (8.7C, 08-3, 9) The drawing below shows how 3 squares can be joined at their vertices to form a right triangle.
What is the area in square centimeters of the largest square?
A 37 cm²
B 210 cm²
C 420 cm²
D 1369 cm² ß
4. (8.7C, 09-32, 10) Which group of squares can be joined at their vertices to form a right triangle?
A ß C
B D
/ 6. (8.7C, 08-3, 10) Look at the drawing shown below.
If is a right triangle formed by the placement of three squares, what is the area of the shaded square?
A 28 mm²
B 125 mm²
C 784 mm² ß
D 64 mm²
8.7C The student is expected to use pictures or models to demonstrate the Pythagorean Theorem.
7. (8.7C, 09-49, 10) The three squares shown below are joined at their vertices to form a right triangle.What is the area of the shaded square?
A 80 cm² ß C 2 cm²
B 352 cm² D 658 cm² / 9. (8.7C, 04-36, 10) Look at the right triangle shown below. Which of the following could be the triangle’s dimensions?
A 12, 16.8, 18.2
B 5.4, 10.6, 16
C 1.2, 1.6, 2 ß
D 8, 10, 12.5
8. (8.7C, 06-15, 10) The drawing below shows how 3 squares can be joined at their vertices to form a right triangle.
Which is closest to the area in square inches of the largest square?
A 1914 in.²
B 233 in.²
C 210 in.²
D 1073 in.² ß / 10. (8.7C, 03-13, 10) The sides of squares can be used to form triangles. The areas of the squares that form right triangles have a special relationship.
Using the dimensions of the squares shown below, determine which set of squares will form a right triangle.
A C ß
B D
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