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EXAMPLE 1

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. Use the Pythagorean Theorem to find the slant height l. 1. l 2 = h 2 +( b) 2. 2. 1. Substitute for h and b. 2.

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EXAMPLE 1

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  1. A regular square pyramid has a height of 15centimeters and a base edge length of 16centimeters. Find the area of each lateral face of the pyramid Use the Pythagorean Theorem to find the slant height l. 1 l2 = h2 +( b)2 2 1 Substitute for h and b. 2 Find the area of a lateral face of a pyramid EXAMPLE 1 SOLUTION Write formula. l2 =152 +82

  2. The area of each triangular face is ANSWER 1 1 A = bl = (16)(17) = 136square centimeters. 2 2 Find the area of a lateral face of a pyramid EXAMPLE 1 l2 = 289 Simplify. l = 17 Find the positive square root.

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

  4. S = B + Pl = 150√ 3 + (60)(14) 1 1 2 2 = 150√ 3 + 420 ANSWER The surface area of the regular hexagonal pyramid is about 679.81 ft2. Find the surface area of a pyramid EXAMPLE 2 Formula for surface area of regular pyramid. Substitute known values. Simplify. ≈ 679.81 Use a calculator.

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

  6. 1 1 1 l2 = h2 +( b)2 2 2 2 The area of each lateral face isA = bl = (8) (7.3) =29.2m2 ANSWER 1 Substitute for h and b. 2 for Examples 1 and 2 GUIDED PRACTICE Write formula. l2 = (4.8) + (5.5)2 l2 = 7.5 Find the positive square root.

  7. 1 1 2 2 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 5.5m and the perimeter p is 5.8 = 40m so , the area of the base is (5.5) (40) = 110m. Then find the surface area for Examples 1 and 2 GUIDED PRACTICE 2. Find the surface area of the regular pentagonal pyramid shown. SOLUTION

  8. 1 1 2 2 = 110 + (40)7.3 S = b + pl ANSWER The surface area of the rectangle pentagon pyramid is 256m2 for Examples 1 and 2 GUIDED PRACTICE Formula for surface area of regular pyramid. Substitute known values. = 256 Use a calculator.

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