Main Idea and New Vocabulary Key Concept Surface

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 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

Surface Area of Rectangular Prisms 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.

Find the surface area of the rectangular prism. A. 22 in 2 B. 36 in 2 C. 76 in 2 D. 80 in 2

Surface Area of Rectangular Prisms Find the surface area of the rectangular prism. Replace b with 10, w with 8, and h with 12. surface area = 2 bh + 2 bw + 2 hw = 2 • 10 • 12 + 2 • 10 • 8 + 2 • 12 • 8 = 240 + 160 + 192 = 592 Answer: The surface area of the prism is 592 square inches.

Find the surface area of the rectangular prism. A. 18 in 2 B. 25 in 2 C. 30 in 2 D. 46 in 2

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 = 2 bh + 2 bw + 2 hw = 2 • 11 • 6 + 2 • 11 • 8 + 2 • 6 • 8 = 132 + 176 + 96 = 404 in 2

Step 2 Find the number of square inches the wrapping paper will cover. 1 ft 2 = 1 ft × 1 ft = 12 in. × 12 in. Replace 1 ft with 12 in. = 144 in 2 Multiply. The sheet of wrapping paper is 4 feet by 1 foot or 4 square feet. So, 4 square feet is equal to 4 × 144 or 576 square inches. Answer: Since 576 > 404, Diana has enough wrapping paper to wrap the box.

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. A. Yes; since 310 in 2 > 288 in 2, she has enough fabric. B. No, since 288 in 2 < 310 in 2, she does not have enough fabric.

Surface Area of Triangular Prisms 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? 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 1 __ 2 • 10 • 7 or 35. 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 + 103. 2 + 120 or 396. 4 square feet.

Surface Area of Triangular Prisms Answer: So, 396. 4 square feet of fabric was used.

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? A. 141. 5 ft 2 C. 163 ft 2 B. 145 ft 2 D. 170 ft 2