Instructions: Read Each Question Carefully and Select the Correct Answer

SD 9-12 Measurement
03/20/2009

Student Name: ______

Class: ______

Date: ______

Instructions: Read each question carefully and select the correct answer.

SD 9-12 Measurement – Test, Answer Key, & Study Guide Page 32 of 33

1. A drawing of geometric shapes includes a triangle. What is the area of the triangle if its height is 15 in., its base is 17 in., and its other two sides are approximately 17.24 in.? Round your answer to the nearest tenth, if necessary.

A. 293.1 in.2

B. 146.5 in.2

C. 255.0 in.2

D. 127.5 in.2

SD 9-12 Measurement – Test, Answer Key, & Study Guide Page 32 of 33

2. Roger created a model parallelogram. The base is equal to 12.5 meters and the height is equal to 8.1 meters.
What is the area of Roger's parallelogram?

A. 50.625 square meters

B. 41.2 square meters

C. 101.25 square meters

D. 202.5 square meters

3. The top of a monument is in the shape of a pyramid. The base of the pyramid is a square with sides 6.8 meters long. The height of each triangular face is 8.8 meters long.
What is the surface area of the monument?
Round the answer to the nearest hundredth when necessary.

A. 119.68 square meters

B. 285.60 square meters

C. 165.92 square meters

D. 183.52 square meters

SD 9-12 Measurement – Test, Answer Key, & Study Guide Page 32 of 33

4. Use the picture to answer the question. What is the measure of RQP to the nearest 5º ?

A. 65º

B. 75º

C. 115º

D. 125º

SD 9-12 Measurement – Test, Answer Key, & Study Guide Page 32 of 33

A. 74.1 m

B. 7.4 m

C. 37.1 m

D. 3.7 m

6. Find the volume of a sphere with diameter = 12.4 feet. Round to the nearest cubic foot. Use = 3.14.

A. 139,917 ft3

B. 17,490 ft3

C. 7,982 ft3

D. 998 ft3

7. Find the area of the parallelogram.

A. 22 cm2

B. 11 cm2

C. 24 cm2

D. 33 cm2

8. What is the area of the figure?

A. 5,917.6726 square meters

B. 641.83 square meters

C. 342.062 square meters

D. 69.613 square meters

9. What is the value of x for the right triangle?

A. 5 centimeters

B. 8 centimeters

C. 10 centimeters

D. 32 centimeters

10. Find the surface area of the figure.

A. 144 square meters

B. 131.88 square meters

C. 37.68 square meters

D. 602.88 square meters

11. This is the layout of the McDougal's backyard. The scale is 1 centimeter to 5 meters. The actual area of the deck is 350 square meters. The length of the deck is 35 meters.

What is the area of the deck on the layout?

A. 14 square centimeters

B. 87.5 square centimeters

C. 17.5 square centimeters

D. 70 square centimeters

12. What is the circumference of the circle?

Round your answer to the nearest hundredth.

A. 34.54 cm

B. 379.94 cm

C. 69.08 cm

D. 484 cm

13. What is the area of the trapezoid?

A. 43 157/189 square inches

B. 21 173/189 square inches

C. 15 43/63 square inches

D. 28 4/27 square inches

14. What is the area of the circle?

Round your answer to the nearest hundredth.

A. 26.38 square meters

B. 55.39 square meters

C. 13.19 square meters

D. 221.56 square meters

15. A building has the shape of a rectangular prism. The length is 12 dam, the width is 9 dam, and the height is 15 dam.
What is the volume of the building?

A. 5,086.8 cubic dekameters

B. 540 cubic dekameters

C. 1,620 cubic dekameters

D. 423 cubic dekameters

16.
What is the base of the triangular prism?

A. 31104 meters

B. 6 meters

C. 3 meters

D. 1.5 meters

17. What is the volume of the cylinder?

A. 785,000 cubic centimeters

B. 15,700 cubic centimeters

C. 31,400 cubic feet

D. 1,570,000 cubic feet

18. What is the value of x?

A. 24.8 feet

B. 32.24 feet

C. 14.4 feet

D. 7.2 feet

19. What is the surface area of the figure?

A. 936 square meters

B. 866 square meters

C. 450 square meters

D. 20280 square meters

20. Ernesto mailed a poster in a cylinder. The radius of the cylinder was 2.5 inches. The height of the cylinder was 18.6 inches.
What was the surface area of the cylinder?

A. 331.27 square inches

B. 307.72 square inches

C. 769.3 square inches

D. 311.65 square inches

21. We built a pyramid with a triangular base. The area of the base is 12 square feet. The height of the pyramid is 16 feet.
What is the volume of the pyramid?

A. 192 cubic feet

B. 96 cubic feet

C. 32 cubic feet

D. 64 cubic feet

22. What is the volume of the cone?

Round your answer to the nearest hundredth when necessary.

A. 284.86 cubic millimeters

B. 189.91 cubic millimeters

C. 158.26 cubic millimeters

D. 2215.58 cubic millimeters

SD 9-12 Measurement – Test, Answer Key, & Study Guide Page 32 of 33

SD 9-12 Measurement
Answer Key
03/20/2009

1. D Area of Triangle - B

2. C Area of Parallelogram - C

3. C Surface Area of a Pyramid

4. A Accuracy - C

5. D Arc Length

6. D Volume of Spheres

7. A Area of Parallelogram - B

8. C Area of Parallelogram - A

9. C Area of Triangle - A

10. B Surface Area

11. A Scale Drawing - B

12. C Circumference - B

13. B Area of Trapezoid

14. B Area of Circle

15. C Volume of Rectangular Prisms

16. B Volume of Triangular Prism

17. A Volume of Cylinders

18. D Area of Rectangle - D

19. B Surface Area of a Prism

20. A Surface Area of a Cylinder

21. D Volume of Pyramids

22. B Volume of Cone

SD 9-12 Measurement – Test, Answer Key, & Study Guide Page 32 of 33

Study Guide
SD 9-12 Measurement
03/20/2009

Area of Triangle - B
This skill requires the student to find the area of a triangle, which is one half the area of a rectangle that has the same base and height.
The area of a rectangle can be found by multiplying its base by its height.

If a rectangle is divided in half along its diagonal, each triangle formed is half the area of the rectangle.

A regular triangle has three 60-degree angles, and sides that are all the same length. The area of a regular triangle is also one half the area of a rectangle with the same base and height.

The formula for the area of a triangle is:

Remember: Units for area are always squared. Examples: ft2 , in.2 , m2
Example 1: What is the area of a triangle if its base is 13 ft and its height is 10 ft?

Step 1: Write the formula for the area of a triangle.
Step 2: Substitute 13 ft for the base and 10 ft for the height in the formula.
Step 3: Find the product of 13 ft and 10 ft.
Step 4: Multiply 130 by 1/2 (or divide 130 by 2).
Answer: 65 ft2
Example 2: The side of a hay storage building is in the shape of a triangle. What is the area of the side of the building if its base is 10 ft, its height is 12 ft, and the lengths of the other two sides are 13 ft?

Step 1: Write the formula for the area of a triangle. As you can see from the formula, the lengths of the other two sides, besides the base, are not needed to calculate the area.
Step 2: Substitute 10 ft for the base and 12 ft for the height in the formula.
Step 3: Find the product of 10 ft and 12 ft.
Step 4: Multiply 120 by 1/2.
Answer: 60 ft2
An activity that can help reinforce the concept of area of a triangle is to show students several examples of triangles with the height and lengths of all three sides given. Ask them to write down the equations that would allow them to find the area of each triangle, reminding them that the only two dimensions they need are the height and base.

Area of Parallelogram - C
A parallelogram is a quadrilateral (a four-sided figure) with two pairs of parallel and congruent sides. Area is the measure, in square units, of the interior region of a two-dimensional figure.

To find the area of a parallelogram, multiply the base(b) by the height(h). The base is the length of either the top or bottom. The height is the length of a line going from the base at a right angle to the opposite side. Here is the formula:

Area of a parallelogram = (base) x (height)
Example 1: Find the area of a parallelogram with a base equal to 5 feet and a height equal to 2 feet?

Area = 5 feet x 2 feet = 10 square feet
Answer: 10 square feet
Example 2: Find the area of a parallelogram with a base equal to 5 meters and a height equal to 6 meters?
Area = 5 meters x 6 meters = 30 square meters
Answer: 30 square meters

Surface Area of a Pyramid
A pyramid is a three-dimensional figure whose base is a polygon and whose other faces are triangles that share a common vertex. Surface area is the total area of the faces (including bases) of a three-dimensional figure.

To find the surface area of a pyramid, you need to find the area of the base and the area of the sides and add them up. It may be helpful to visualize the parts of a square pyramid and the parts of a triangular pyramid:

To find the area of a square with side length b, use the following formula.
Area of a square = length x length = b x b
If the area of the square is already known, the length of a side can be found by taking the square root of the area.
To find the area of a triangle, use the following formula.
Area of a triangle = 1/2 x (base) x (height)
Example 1: Find the surface area of a pyramid with a square base with sides 8 ft long and the height of each triangular face is 7 ft long.
(1) 8 x 8 = 64 square feet
(2) (1/2) (8 feet) (7 feet) = 28 square feet
(3) 64 + 28 + 28 + 28 + 28 = 176 square feet
Step 1: Determine the area of the base. The base of this pyramid is a square. The side length is 8 feet, so multiply 8 x 8 to get the area of base. The area of the base is 64 square feet.
Step 2: Determine the surface area of one of the triangular faces. The sides of the base are 8 ft long, so the base of the triangular face is 8 ft long. The height is given as 7 ft. Substitute the values of the base and height into the formula for the area of a triangle to get the area of one triangular face.
Step 3: Add the areas of all faces (including the base) together. There is one base and four faces.
Total surface area = 64 + 28 + 28 + 28 + 28 = 176 square feet.
We can similarly determine the area of a triangular pyramid if all faces including the base are congruent. If we are given the surface area of one of the faces, we can multiply that times the number of faces (4) to determine the total surface area for the pyramid.
Example 2: The area of one face of a triangular pyramid is 32 square centimeters. All of the faces, including the base are congruent. What is the surface area of the triangular pyramid?
There are 4 triangles in a triangular pyramid, so multiply 32 x 4 to get the surface area of the pyramid.
32 x 4 = 128
The surface area of the triangular pyramid is 128 square centimeters.
When given the length of the sides of the base and the height of each face, you can determine the surface area of one face and multiply that number by 4 (the number of faces), when the base and faces are congruent.

Accuracy - C
Area is the measure, in square units, of the interior region of a two-dimensional figure.

The formula for area of a rectangle is:
Area (A) = length x width.
The formula for the area of a triangle is:
Area (A) = (1/2) x base x height
Example 1: What is the area of the shaded region? Round your answer to the nearest square centimeter.

(1) 18.85 - 6.7 - 5.89 = 6.26 cm
(2) 10.07 - 3 - 3.5 = 3.57 cm
(3) Area = Length x width
(4) Area = 6.26 x 3.57 = 22.3482
(5) 22.3482 ~ 22
Step 1: Determine the length of the shaded region by subtracting 5.89 and 6.7 from 18.85. The length of the shaded region is 6.26 cm.
Step 2: Determine the width of the shaded region by subtracting 3 and 3.5 from 10.07. The width of the shaded region is 3.57 cm.
Step 3: Select the appropriate area formula. We are finding the area of a rectangle, so we need the formula for the area of a rectangle.
Step 4: Substitute the values for the length and width of the shaded region into the formula for the area of a rectangle and multiply.
Step 5: The directions required rounding the answer to the nearest square centimeter, so 22.3482 rounds to 22 square centimeters. The ~ symbol means approximately.
Answer: 22 square centimeters
Example 2: The area of the shaded region is 25% of the area of the outer figure. What is the area of the shaded region? Round your answer to the nearest square millimeter.

(1). (1/2) x 16.232 x 13.62 = 110.53992
(2). 110.53992 x 25% = 110.53992 x 0.25 = 27.63498
(3). 27.63498 ~ 28
Step 1: Determine the area of the outer triangle using the formula for the area of a triangle. The height of the triangle is 13.62 millimeters and the base of the triangle is 16.232 millimeters. The area of the outer triangle is 110.53992 square millimeters.
Step 2: Since the area of the shaded region is 25% of the area of the outer triangle, multiply the area of the outer triangle by 25%. Before multiplying by 25%, we must convert 25% into a decimal by moving the decimal point two places to the left. 25% equals 0.25.
Step 3: Round the answer to the nearest square millimeter. 27.63498 rounds to 28.
Answer: 28 square millimeters
A protractor is a tool that is used to measure the degree of an angle.
Example 3: What is the measurement of the angle to the closest 5º ?

Solution: Since the angle opens to the right of the protractor, we are going to use the set of numbers on the outside of the protractor. The measure of the angle is between 20º and 30º and just a bit past 25º . Therefore, we would round the measure to 25º .