Five-Minute Check (over Lesson 12–3)

Main Idea and Vocabulary

Key Concept: Surface Area of a Rectangular Prism

Example 1:Find Surface Area

Example 2:Find Surface Area

Example 3:Real-World Example

Example 4:Use the Pythagorean Theorem

• surface area

• Find the surface areas of rectangular prisms.

Find Surface Area

Find the surface area of the rectangular prism.

You can use a net of the rectangular prism to find its surface area. There are three pairs of congruent faces.

• top and bottom

• front and back

• two sides

Find Surface Area

Faces Area

top and bottom 2(6 ● 2) = 24

Answer: The surface area is 72 square centimeters.

sum of the areas 24 + 36 + 12 = 72

front and back 2(6 ● 3) = 36

two sides 2(2 ● 3) = 12

1. A

2. B

3. C

4. D

A B C D

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A. 16 ft2

B. 108 ft2

C. 150 ft2

D. 162 ft2

Find the surface area of the rectangular prism.

Find Surface Area

Find the surface area of the rectangular prism.

Replace ℓ with 10, w with 8, and h with 12.

surface area = 2ℓw + 2ℓh + 2wh

= 2 ●10 ● 8 + 2 ● 10 ● 12 + 2 ● 8 ● 12

= 160 + 240 + 192 Multiply first. Then add.

= 592

Answer: 592 in2

1. A

2. B

3. C

4. D

A B C D

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A. 22 cm2

B. 210 cm2

C. 254 cm2

D. 312 cm2

Find the surface area of the rectangular prism.

BOXES Drew is putting together a cardboard box that is 9 inches long, 6 inches wide, and 8 inches high. He bought a roll of wrapping paper that is 1 foot wide and 3 feet long. Did he buy enough to wrap the box? Justify your answer.

Step 1 Find the surface area of the box.

Replace ℓ with 9, w with 6, and h with 8.

surface area = 2ℓw + 2ℓh + 2wh

= 2 ● 9 ● 6 + 2 ● 9 ● 8 + 2 ● 6 ● 8

= 348 in2

Answer: Since 348 in2 < 432 in2, Drew bought enough paper.

Step 2 Find the area of the wrapping paper.

area = 12 in. ● 36 in. or 432 in2

1 ft 3 ft

1. A

2. B

3. C

4. D

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A. yes; 360 > 310

B. yes; 328 > 295

C. no; 360 < 412

D. no; 310 < 360

Find the surface area of the rectangular prism.

The width and length of the prism are given. To find surface area, you need to find the height of the prism. Notice that the diagonal, length, and height of the front face of the prism form a right triangle.

Use the Pythagorean Theorem

c2 = a2 + b2 Pythagorean Theorem

The height of the prism is 6.3 meters. Find the surface area.

Use the Pythagorean Theorem

72 = 32 + b2 Replace c with 7 and a with 3.

49 = 9 + b2 Evalute powers.

49 – 9 = 9 + b2 – 9 Subtract 9 from each side.

40 = b2 Simplify.

±6.3 = b Simplify.

Definition of square root

surface area = 2ℓw + 2ℓh + 2wh

Answer: The surface area of the prism is 130.8 square meters.

Use the Pythagorean Theorem

= 2 • 3 • 5 + 2 • 3 • 6.3 + 2 • 5 • 6.3

= 30 + 37.8 + 63 Multiply first. Then add.

= 130.8

1. A

2. B

3. C

4. D

A B C D

0% 0%0%0%

Find the surface area of a rectangular prism that has width 5 feet, diagonal 13 feet, and height 2 feet.

A. 188 square feet

B. 215 square feet

C. 241 square feet

D. 256 square feet

End of the Lesson

Five-Minute Check (over Lesson 12–3)

Image Bank

Math Tools

The Pythagorean Theorem

1. A

2. B

3. C

4. D

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(over Lesson 12-3)

A.

B.

C.

D.

Solve the problem by making a model.

1. A

2. B

3. C

4. D

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(over Lesson 12-3)

A. 16

B. 12

C. 20

D. 24

Solve the problem by making a model.A sports collector shop arranges four of its most expensive baseball cards in the top display case four in a row. In how many different ways can four baseball cards be arranged in a row?

1. A

2. B

3. C

4. D0% 0%0%0%

(over Lesson 12-3)

A. $130.25

B. $563

C. $295.25

D. $212.75

Solve the problem by making a model.Helen wrote checks for $26.75, $134, and $52. If she now has $82.50 in her checking account, how much did she have to begin with?

1. A

2. B

3. C

4. D

A B C D

0% 0%0%0%

(over Lesson 12-3)

A. 81 ft

B. 64 ft

C. 40 ft

D. 34 ft

Mr. Green has a square flowerbed that is 8 feet long on each side. He puts a stone border around it that is 1 foot wide. What is the perimeter of the stone border?