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## Warm Up

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**Preview**Warm Up California Standards Lesson Presentation**Warm Up**Identify the figure described. 1.two parallel congruent faces, with the other faces being parallelograms 2. a polyhedron that has a vertex and a face at opposite ends, with the other faces being triangles prism pyramid**California**Standards AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2w + 2l, A = bh, C = pd–the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). Also covered:AF3.2 1 2**Vocabulary**surface area net**The surface area of a three-dimensional figure is the sum of**the areas of its surfaces. To help you see all the surfaces of a three-dimensional figure, you can use a net. A net is an arrangement of two-dimensional figures that can be folded to form a three-dimensional figure.**Helpful Hint**To find the area of the curved surface of a cylinder, multiply its height by the circumference of the base. The surface area of a cylinder equals the sum of the area of its bases and the area of its curved surface.**Additional Example 1: Finding the Surface Area of a Prism**Find the surface area S of the prism. A. Method 1: Use a net. Draw a net to help you see each face of the prism. Use the formula A = lw to find the area of each face.**Add the areas of each face.**Additional Example 1A Continued A: A = 5 2 = 10 B: A = 12 5 = 60 C: A = 12 2 = 24 D: A = 12 5 = 60 E: A = 12 2 = 24 F: A = 5 2 = 10 S = 10 + 60 + 24 + 60 + 24 + 10 = 188 The surface area is 188 in2.**Additional Example 1: Finding the Surface Area of a Prism**Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. Find the area of the front, top, and side, and multiply each by 2 to include the opposite faces.**Additional Example 1B Continued**Front: 9 7 = 63 63 2 = 126 Top: 9 5 = 45 45 2 = 90 Side: 7 5 = 35 35 2 = 70 S = 126 + 90 + 70 = 286 Add the areas of each face. The surface area is 286 cm2.**S = s2 + 4 ( bh)**1 1 __ __ S = 72 + 4 ( 78) 2 2 Substitute. Additional Example 2: Finding the Surface Area of a Pyramid Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) S = 49 + 4 28 S = 49 + 112 S = 161 The surface area is 161 ft2.**Additional Example 3: Finding the Surface Area of a Cylinder**Find the surface area S of the cylinder. Write your answer in terms of . ft S = area of curved surface + (2 area of each base) S = (h 2r) + (2 r2) Substitute 7 for h and 4 for r. S = (7 24)+ (2 42) S = (7 2 4)+ (2 16) Simplify the power.**Additional Example 3 Continued**Find the surface area S of the cylinder. Write in terms of . S = 56 + 32 Multiply. S= (56 + 32)p Use the Distributive Property. S= 88p The surface area is about 88p ft2.**Find the area of the front, top, and side, and multiply each**by 2 to include the opposite faces. Check It Out! Example 1 Find the surface area S of each prism. B. Method 2: Use a three-dimensional drawing. top side front 8 cm 10 cm 6 cm**Check It Out! Example 1B Continued**top side front 8 cm 10 cm 6 cm Front: 8 6 = 48 48 2 = 96 Top: 10 6 = 60 60 2 = 120 Side: 10 8 = 80 80 2 = 160 S = 160 + 120 + 96 = 376 Add the areas of each face. The surface area is 376 cm2.**10 ft**5 ft S = s2 + 4 ( bh) 5 ft 1 1 __ __ S = 52 + 4 ( 510) 2 2 Substitute. Check It Out! Example 2 Find the surface area S of the pyramid. S = area of square + 4 (area of triangular face) 10 ft S = 25 + 4 25 5 ft S = 25 + 100 S = 125 The surface area is 125 ft2.**Check It Out! Example 3**Find the surface area S of the cylinder. Write your answer in terms of . 6 ft 9 ft S = area of lateral surface + (2 area of each base) S = (h 2r) + (2 r2) Substitute 9 for h and 6 for r. S = (9 26)+ (2 62) S = (9 2 6) + (2 36) Simplify the power.**Check It Out! Example 3 Continued**Find the surface area S of the cylinder. Write your answer in terms of . S = 108 + 72 Multiply. S= (108 + 72)p Use the Distributive Property. S= 180p The surface area is about 180pft2.**Lesson Quiz**Find the surface area of each figure. Use 3.14 as an estimate for . 1. rectangular prism with base length 6 ft, width 5 ft, and height 7 ft 2. cylinder with radius 3 ft and height 7 ft 3. Find the surface area of the figure shown. 214 ft2 ≈188.4 ft2 208 ft2