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You found areas of polygons. • Find lateral areas and surface areas of prisms. • Find lateral areas and surface areas of cylinders. • lateral face • lateral edge • base edge • altitude • height • lateral area • axis • composite solid Lateral Area of a Prism Find the lateral area of the regular hexagonal prism. The bases are regular hexagons. So the perimeter of one base is 6(5) or 30 centimeters. Lateral area of a prism P = 30, h = 12 Multiply. Answer: The lateral area is 360 square centimeters. Find the lateral area of the regular octagonal prism. A. 162 cm2 B. 216 cm2 C. 324 cm2 D. 432 cm2 Surface Area of a Prism Find the surface area of the rectangular prism. Surface Area of a Prism Surface area of a prism L = Ph Substitution Simplify. Answer: The surface area is 360 square centimeters. Find the surface area of the triangular prism. A. 320 units2 B. 512 units2 C. 368 units2 D. 416 units2 Lateral Area and Surface Area of a Cylinder Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. L = 2rh Lateral area of a cylinder = 2(14)(18) Replace r with 14 and h with 18. ≈ 1583.4 Use a calculator. Lateral Area and Surface Area of a Cylinder S = 2rh + 2r2 Surface area of a cylinder ≈ 1583.4 + 2(14)2 Replace 2rh with 1583.4 and r with 14. ≈ 2814.9 Use a calculator. Answer: The lateral area is about 1583.4 square feet and the surface area is about 2814.9 square feet. Find the lateral area and the surface area of the cylinder. Round to the nearest tenth. A. lateral area ≈ 1508 ft2 and surface area ≈ 2412.7 ft2 B. lateral area ≈ 1508 ft2 and surface area ≈ 1206.4 ft2 C. lateral area ≈ 754 ft2 and surface area ≈ 2412.7 ft2 D. lateral area ≈ 754 ft2 and surface area ≈ 1206.4.7 ft2 Find Missing Dimensions MANUFACTURING A soup can is covered with the label shown. What is the radius of the soup can? L = 2rh Lateral area of a cylinder 125.6 = 2r(8) Replace L with 15.7 ● 8 and h with 8. 125.6 = 16r Simplify. 2.5 ≈ r Divide each side by 16. Find Missing Dimensions Answer: The radius of the soup can is about 2.5 inches.