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Surface Area of Pyramids Pyramid – A polyhedron with all faces except one intersecting a vertex. Pyramids are named for their bases, which can be a polygon of any variety.

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Surface Area of Pyramids Lateral Faces – The faces that intersect at the vertex. For a pyramid, they are all triangles. Lateral Edges – The edges of the lateral faces that have the vertex as an endpoint. Altitude – The segment from the vertex that is perpendicular to the base.

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Surface Area of Pyramids Axis – A line segment from the vertex of a pyramid to the center of its base. Right Pyramid – A pyramid in which the altitude and the axis are the same segment. In this case, the base does not have to be a regular polygon.

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Surface Area of Pyramids Regular pyramid – A pyramid in which the altitude and the axis are the same segment and the base is a regular polygon. In a regular pyramid, each of the lateral faces is a congruent isosceles triangle. Slant Height – The height of each lateral face of the pyramid. It is represented by l (lower case L).

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Surface Area of Pyramids Lateral Area of a Regular Pyramid If a regular pyramid has a lateral area of L square units, a slant height of l units, and its base has a perimeter of P units, then L = (1/2)*P*l

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Example 5-1c CAMPING A pyramidal shaped tent is put up by two campers. The square base is 7 feet on a side and the slant height of the tent is 7.4 feet. Find the lateral area of the tent. Answer: 103.6 ft 2

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Surface Area of Pyramids Surface Area of a Regular Pyramid If a regular pyramid has a surface area of T square units, a slant height of l units, and its base has a perimeter of P units and an area of B square units, then T = (1/2)*P*l + B

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Example 5-2d Find the surface area of the regular pyramid to the nearest tenth. Answer: 89.8 m 2

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Example 5-3f Find the surface area of the regular pyramid. Answer: about 298.2 cm 2

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