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12-5 Surface Areas of Pyramids

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Objectives: Find lateral areas of regular pyramids Find surface areas of regular pyramids

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Lateral area of regular pyramids If L represents the lateral area & X represents the slant height and P is perimeter of the base then L=1/2(P)(X) 90° slant height

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Example: Find Lateral Area 90° 6 1010 1.P=10 x 4 2.L=1/2 x 40 x 6 3.L=120units sq AWESOME!!!

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Surface area of a regular pyramid l If a regular pyramid has a surface area of T sq units, a slant height of l units, and its base has a perimeter of P units, then T=1/2 x P x l + B

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Example: Find Surface area 5 20 1.20 x 4= 80 2.B= 20 x 20= 400 3.T= ½ x 80 x 5 + 400 4.T= 400

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Surface are of pentagonal pyramid The altitude, slant height, and apothem form a right triangle. Use Pythagorean Theorem to find the apothem. apothem 36° 15 17 17²= a² + 15² 8= a 8 s use tan 1.tan 36°= (1/2 x s)/ 8 2.8(tan 36°)= 1/2 x s 3.16(tan 36°)= s 4.11.6= s

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Continued... Find the perimeter and area of the base 1.P= 5s 2.P= 5 x 11.6 or 58 3.B= ½ x Pa 4.B= ½ x 58 x 8 or 232 Find perimeter and area of base 1.T= 1/2 x Pl + B 2.T= (½ x 58 x 17) + 232 3.T= 726.5 units sq

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