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EXAMPLE 1 Find the area of a lateral face of a pyramid SOLUTION Use the Pythagorean Theorem to find the slant height l. l 2 =15 2 +8 2 Write formula. l 2 = h 2 +( b) 2 1 2 A regular square pyramid has a height of 15 centimeters and a base edge length of 16 centimeters. Find the area of each lateral face of the pyramid Substitute for h and b. 1 2

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EXAMPLE 1 Find the area of a lateral face of a pyramid l = 17 Find the positive square root. l 2 = 289 Simplify. A = bl = (16)(17) = 136 square centimeters. 1 2 1 2 The area of each triangular face is ANSWER

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EXAMPLE 2 Find the surface area of a pyramid SOLUTION Find the surface area of the regular hexagonal pyramid. First, find the area of the base using the formula for the area of a regular polygon, aP. The apothem a of the hexagon is 5√ 3 feet and the perimeter P is 6 10 = 60 feet. So, the area of the base B is (5√ 3)(60) = 150√ 3 square feet. Then, find the surface area. 1 2 1 2

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EXAMPLE 2 Find the surface area of a pyramid Formula for surface area of regular pyramid. ≈ 679.81 Substitute known values. Simplify. Use a calculator. = 150√ 3 + (60)(14) 1 2 = 150√ 3 + 420 S = B + Pl 1 2 The surface area of the regular hexagonal pyramid is about 679.81 ft 2. ANSWER

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GUIDED PRACTICE for Examples 1 and 2 1. Find the area of each lateral face of the regular pentagonal pyramid shown. Use the Pythagorean theorem to find the slant height l SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 l 2 = (4.8) + (5.5) 2 Write formula. l 2 = h 2 +( b) 2 1 2 Substitute for h and b. 1 2 Find the positive square root. l 2 = 7.5 The area of each lateral face is A = bl = (8) (7.3) =29.2 m 2 1 2 1 2 ANSWER

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GUIDED PRACTICE for Examples 1 and 2 2. Find the surface area of the regular pentagonal pyramid shown. First find the area of the base using the formula for the area of a regular polygon, AP the apothem a of the pentagon is 5.5 m and the perimeter p is 5.8 = 40m so, the area of the base is (5.5) (40) = 110 m. Then find the surface area 1 2 1 2 SOLUTION

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GUIDED PRACTICE for Examples 1 and 2 S = b + pl 1 2 1 2 = 110 + (40)7.3 = 256 Formula for surface area of regular pyramid. Substitute known values. Use a calculator. The surface area of the rectangle pentagon pyramid is 256 m 2 ANSWER

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