Main Idea and New Vocabulary

Key Concept: Surface Area of a Rectangular Prism

Example 1: Surface Area of Rectangular Prisms

Example 2: Surface Area of Rectangular Prisms

Example 3: Real-World Example

Example 4: Surface Area of Triangular Prisms

• Find the surface areas of prisms.

• surface area

Surface Area of Rectangular Prisms

Find the surface area of the rectangular prism.

There are three pairs of congruent faces.

• top and bottom

• front and back

• two sides

Faces Area

top and bottom 2(6 • 2) = 24

front and back 2(6 • 3) = 36

two sides 2(3 • 2) = 12

sum of the areas 24 + 36 + 12 = 72

Answer: The surface area of the prism is 72 square

centimeters.

Surface Area of Rectangular Prisms

A. 22 in2

B. 36 in2

C. 76 in2

D. 80 in2

Find the surface area of the rectangular prism.

Find the surface area of the rectangular prism.

Surface Area of Rectangular Prisms

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

surface area = 2bh + 2bw + 2hw

= 2 • 10 • 12 + 2 • 10 • 8 + 2 • 12 • 8

= 240 + 160 + 192

= 592

Answer: The surface area of the prism is 592 squareinches.

A. 18 in2

B. 25 in2

C. 30 in2

D. 46 in2

Find the surface area of the rectangular prism.

GIFTS Diana has a gift box that is 11 inches long, 8 inches wide, and 6 inches tall. She has a sheet of wrapping paper that is 4 feet long by 1 foot wide. Does she have enough wrapping paper to wrap the box? Justify your answer.

Step 1 Find the surface area of the gift box.

Replace b with 11, w with 8, and h with 6.

surface area = 2bh + 2bw + 2hw

= 2 • 11 • 6 + 2 • 11 • 8 + 2 • 6 • 8

= 132 + 176 + 96

= 404 in2

Step 2 Find the number of square inches the wrapping paper will cover.

1 ft2 = 1 ft × 1 ft

= 12 in. × 12 in. Replace 1 ft with 12 in.

= 144 in2 Multiply.

The sheet of wrapping paper is 4 feet by 1 footor 4 square feet. So, 4 square feet is equal to4 × 144 or 576 square inches.

Answer: Since 576 > 404, Diana has enoughwrapping paper to wrap the box.

A. Yes; since 310 in2 > 288 in2, she has enough fabric.

B. No, since 288 in2 < 310 in2, she does not have enough fabric.

FABRIC Angela needs to cover a cardboard box that is 15 inches long, 5 inches wide, and 4 inches high with felt. She bought a piece of felt that is 1 foot wide and 2 feet long. Did she buy enough felt to cover the box? Explain.

TENTS Brian’s tent is a triangular prism with a side length of 12 feet and a width of 8.6 feet. The triangular face has a height of 7 feet and a base of 10 feet. How much fabric is used to make the tent?

Surface Area of Triangular Prisms

To find the surface area of the tent, find the area of each face and add.

Surface Area of Triangular Prisms

The area of each triangle is • 10 • 7 or 35.__12

The area of two of the rectangles is 12 • 8.6 or 103.2.

The area of the third rectangle is 12 • 10 or 120.

The sum of the areas of the sides is 35 + 35 + 103.2 + 103.2 + 120 or 396.4 square feet.

Surface Area of Triangular Prisms

Answer: So, 396.4 square feet of fabric was used.

A. 141.5 ft2 C. 163 ft2

B. 145 ft2 D. 170 ft2

SCULPTURES Gilberto has been commissioned to build a sculpture made of geometric figures to sit in front of the art museum. One piece is a triangle prism that will have a length of 8 feet. The triangular bases will have equal side lengths of 5 feet and a height of 4.3 feet. He plans to paint the prism blue. How much surface area will the paint need to cover?