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Surface Area of Pyramids

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ADDITION TO DIAGRAM – NEW VOCAB The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base.

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The lateral faces of a regular pyramid can be arranged to cover half of a rectangle with a height equal to the slant height of the pyramid. The width of the rectangle is equal to the base perimeter of the pyramid.

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Example 1 Find the surface area of the regular pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height. n = 3, s = 14, l = 14

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Example 2 Find the surface area of the regular pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height. n = 6, s = 5.2, l = 13

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Example 3 Find the surface area of the regular pyramid. n represents the number of sides of the base, and s represents the length of one side of the base, and l is the slant height. n = 4, s = 12, l = 13

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Example 4 Work backwards to solve for the missing information. In a rectangular pyramid, one side of the base is 30 in. The slant height of the pyramid is 29 in, and the SA = 4180 square inches. What is the length of the other side of the rectangular base?

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Example 5 Work backwards to solve for the missing information. In a triangular pyramid, the base area is 50 square mm. The slant height of the pyramid is 40 mm, and the SA = 250 square mm. What is the perimeter of the triangular base?

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Example 6 Work backwards to solve for the missing information. In a square pyramid, the slant height is 5 cm, and the SA = 96 square cm. What is the length of one side of the base?

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