WVDE Math 7 G Draw,
Construct, and Describe
Geometrical Figures and Describe
the Relationsips between Them
Test
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General Offline Instructions:
Read each question carefully and decide which answer is correct.
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1.
On a field trip to Washington D.C. your group visited the National Cathedral. You saw a 50 foot telephone pole casting a
shadow. You estimate its shadow to be 10 feet. You also noticed the shadow of the National Cathedral and estimated the
shadow to be 60 feet.
If your estimations are close how tall is the National Cathedral?
A B C D 2.
600 feet
500 feet
300 feet
560 feet
On a field trip to Washington D.C. your group visited the new statue of Martin Luther King Jr called the Stone of Hope. You
saw a 3 foot pole casting a shadow. You estimate its shadow to be 2 feet. You also noticed the shadow of the Stone of
Hope and estimated the shadow to be 20 feet.
If your estimations are close how tall is the Stone of Hope?
A B C D 3.
40 feet
60 feet
26 feet
30 feet
On a field trip to Washington D.C. your group visited the US Capitol. You saw a 60 foot flag pole casting a shadow. You
estimate its shadow to be 10 feet. You also noticed the shadow of the US Capitol and estimated the shadow to be 48 feet.
If your estimations are close how tall is the US Capitol?
A B C D 288 feet
480 feet
600 feet
648 feet
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4.
On a field trip to Washington D.C., your group visited the Washington Monument. You noticed the
shadow of the Washington Monument and estimated the shadow to be 111 feet. You also saw a nearby
telephone pole about fifty-feet tall casting a shadow of 10 feet.
If your estimates are close, how tall is the Washington Monument?
A B C D 1,110 feet
500 feet
611 feet
555 feet
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5.
Your school is remodeling the flower garden near the school entrance. The current shape is drawn below.
Which statement describes how the area of the garden will change if the length changes to 8?
A The area will increase by 6 square units because 2 × 3 = 6
B The area will increase by 2 square units because 8 - 6 = 2
C The area will increase by 9 square units because 3 × 3 = 9
D The area will increase by 24 square units because 3 × 8 = 24
6.
Jerome is 1.5 meters tall, and at a certain time of day, he casts a shadow that is 2 meters. His
friend measures the shadow formed by a nearby flagpole at the same time of day and finds it to be 24
meters.
What is the height of the flagpole?
A 32 meters
B 12 meters
C 8 meters
D 18 meters
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7.
An engineer built a scale model of a storage container.
The volume of the model is 140 cubic inches.
What is the volume of the actual storage container?
A 5,040 cubic inches because 140 × 36 = 5,040
B 1,260 cubic inches because 36 ÷ 4 = 9 and 140 × 9 = 1,260
C 11,340 cubic inches because 36 ÷ 4 = 9 and (4 × 9)(5 × 9)(7) = 11,340
D 102,060 cubic inches because 36 ÷ 4 = 9 and (4 × 9)(5 × 9)(7 × 9) = 102,060
8.
Yolanda is making a scale model of the garden she plans to build in her back yard. The model is 3 inches
wide and 4 inches long. She knows that her actual garden will be 36 feet long.
Which statement correctly describes how Yolanda can determine the width of her garden?
A 27 feet because 36 ÷ 4 = 9 and 9 × 3 = 27
B 48 feet because 36 ÷ 3 = 12 and 12 × 4 = 48
C 32 feet because 36 – 4 = 32
D 35 feet because 36 – 4 + 3 = 35
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9.
A parallelogram is drawn on the grid below.
Which statement describes how the area of the parallelogram will change if the length changes to 9?
A The area will increase by 8 square units because 36 – 28 = 8
B The area will increase by 35 square units because 63 – 28 = 35
C The area will increase by 4 square units because 26 – 22 = 4
D The area will increase by 53 square units because 81 – 28 = 53
10. Tyrone wants to find the height of the tree in his front yard. He decides to measure his shadow and the
shadow of the tree. He drew the diagram below.
What is the height, h, of the tree?
A 54 inches
B 96 inches
C 102 inches
D 150 inches
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11. Jason drew this rectangle.
You drew a rectangle where the length was 3 centimeters greater than Jason’s but the width is
decreased by 1 centimeter.
Which correctly describes how the perimeter and area of your rectangle compares to Jason’s?
A The perimeter is 2 centimeters greater and the area is 9 square centimeters greater than Jason’s.
B The perimeter is 4 centimeters greater and the area is 9 square centimeters greater than Jason’s.
C The perimeter is 2 centimeters less and the area is 9 square centimeters less than Jason’s.
D The perimeter is 4 centimeters less and the area is 4 square centimeters less than Jason’s.
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12. Steve is planning a mountain bike trip. His usual route is a triangle with sides of 6 miles, 9 miles and 5
miles. He would like to modify his route but still travel in a triangle with the same number of miles.
Which route meets Steve's requirements?
A B C D a triangle with sides of 3 miles, 10 miles and 7 miles
a triangle with sides of 8 miles, 3 miles and 9 miles
a triangle with sides of 14 miles, 3 miles and 3 miles
a triangle with sides of 4 miles, 5 miles and 11 miles
13. A city planner created a scale drawing of the land owned by the airport. The scale of the drawing is 3
inches = 200 feet. The section of land is 3,600 feet wide.
Which of these proportions can be used to find the width of the land in the scale drawing?
A B C D 9
14. Your geometry class cut pieces of drinking straws in order to make geometric shapes. You have two
pieces that measure 9 and 12 centimeters.
Which is the range of the lengths of straws that could be used for the third side of a triangle formed by
using your two straws?
A Between 3 and 15 centimeters
B Between 4.5 and 6 centimeters
C Between 3 and 21 centimeters
D Between 18 and 24 centimeters
15. You and your friend drew similar parallelograms.
The perimeter of the smaller parallelogram is 30 centimeters.
What is the perimeter of the larger parallelogram?
A B C D 33 centimeters
36 centimeters
45 centimeters
42 centimeters
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16. A pyramid with a square base is drawn below.
What shape is formed by the cross section of a vertical plane intersecting the pyramid shown between the
apex and the edge of the base?
A B C D Square
Triangle
Rectangle
Trapezoid
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17. Michael drew the rectangle shown below for Math class.
He then draws a similar rectangle using a scale factor of 2:3.
Which of these is the new rectangle Michael draws?
A B C D 12
18. You have a triangular prism with a volume of 63 cubic inches. If you multiply the dimensions of the
prism by 4, how does the volume of the new prism compare to the original one?
A B C D It is 64 times larger
It is 16 times larger
It is 8 times larger
It is 4 times larger
19. Miranda worked in a real estate office during the summer. She went to the courthouse to get a map of a
plot of land for her supervisor. This is the map Miranda received.
She examined the map and noticed a mistake.
What mistake did Miranda find?
A B C D The lengths of the plot cannot form a triangle.
The lengths of the plot should form an acute triangle.
The smallest angle is not opposite the smallest side in the drawing.
The labeled angles in the drawing do not form a triangle.
20. Greg wants to build a triangular shaped bird house using 3 boards in his scrap lumber pile. The boards are
5, 8 and 9 inches wide and of the same length.
Which statement best describes the outcome of Greg's birdhouse project?
A Greg's birdhouse has the shape of an obtuse triangle.
B Greg's birdhouse has the shape of an acute triangle.
C Greg's birdhouse has the shape of a right triangle.
D Greg did not build a birdhouse because the pieces of wood could not form a triangle.
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21. A plane at an angle of 60 degrees slices a cylinder.
Which of the following shapes represents the cross section of the cylinder intersected by the plane?
A B C D 14
22. You made a triangle with sides 14, 21 and 28.
Which of the following are lengths of a triangle similar to your triangle?
A B C D 15, 15 and 25
18, 27 and 36
21, 28 and 35
24, 30 and 36
23. Julie is planning a trip to several colleges near her home. She plans to visit colleges in the four towns on
the map below. One inch on the map equals 12 miles.
What is the actual distance she will travel from Defiance to Findlay if she goes through Bowling Green?
A B C D 72 miles
6 miles
7 miles
84 miles
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24. Look at this diagram of a park.
What is the actual length and width of the park?
A B C D 36 yards by 36 yards
72 yards by 72 yards
144 yards by 144 yards
2 yards by 2 yards
25. An amusement park in Ohio has a scale model of France’s Eiffel Tower. The base of the Eiffel Tower in
France sits on a square base with the legs 125 meters apart along the sides. The scale model in Ohio sits
on a square base with legs that are
meters apart along the sides and is 108 meters tall.
What is the scale factor of Ohio’s Eiffel Tower to the original in France?
A 1 meter to 3 meters
B 1 meter to 1.16 meters
C 2.6 meters to 1 meter
D 3 meters to 1 meter
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26. A rectangular prism has a volume of 36 cubic inches. A new prism is created by multiplying each
dimension of the prism by 3.
Which of these statements is true?
A The volume of the new prism is 108 cubic inches and is 3 times the volume of the old prism.
B The volume of the new prism is 216 cubic inches and is 6 times the volume of the old prism.
C The volume of the new prism is 324 cubic inches and is 9 times the volume of the old prism.
D The volume of the new prism is 972 cubic inches and is 27 times the volume of the old prism.
27. You drew the rectangle below on a piece of poster paper.
Your teacher then asked you to draw another rectangle similar to the first rectangle using a scale factor of
2.
Which statement about the rectangles is true?
A The area of the new rectangle is 80 square inches and is 4 times greater than the area of the first
rectangle.
B The area of the new rectangle is 64 square inches and is 4 times greater than the area of the first
rectangle.
C The area of the new rectangle is 32 square inches and is 2 times greater than the area of the first
rectangle.
D The area of the new rectangle is 40 square inches and is 2 times greater than the area of the first
rectangle.
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28. The Empire State building in New York City is one of the most recognized sights in the United States. As
part of a social studies project, you have chosen to create a scale model of this building. The base of the
Empire state building is 187 feet wide by 424 feet long. You are using a scale of 1 inch = 20 feet to build
your model.
Which rectangle below shows the correct dimensions that you will use as the base of your model?
A B C D 18
29. A hiking group is planning an expedition to the summit of the mountain shown.
On the map, 1 centimeter is equal to 10 miles.
What is the approximate distance the hikers will travel from the base to the summit of the mountain?
A B C D 10 miles
13 miles
0.3 miles
30 miles
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