10.2.2 Surface Area of Pyramids and Cones
Key Objectives • Learn and apply the formula for the surface area of a pyramid. • Learn and apply the formula for the surface area of a cone. Key Terms • The vertex of a pyramid is the point opposite the base of the pyramid. • The base of a regular pyramid is a regular polygon, and the lateral faces are congruent isosceles triangles. • The slant height of a regular pyramid is the distance from the vertex to the midpoint of an edge of the base. • The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. • The vertex of a cone is the point opposite the base. • The axis of a cone is the segment with endpoints at the vertex and the center of the base. • The axis of a right cone is perpendicular to the base. • The axis of an oblique cone is not perpendicular to the base. • The slant height of a right cone is the distance from the vertex of a right cone to a point on the edge of the base. • The altitude of a cone is a perpendicular segment from the vertex of the cone to the plane of the base. Formulas • Lateral Area of a Regular Pyramid The lateral area of a regular pyramid with perimeter P and slant height l is L Pl . = • Surface Area of a Regular Pyramid The surface area of a regular pyramid with lateral area L and base area B is S = L + B , or S Pl B • Lateral Area of a Right Cone The lateral area of a right cone with radius r and slant height l is L = πrl . • Surface Area of a Right Cone The surface area of a right cone with lateral area L and base area B is S = L + B , or S = πrl + πr 2 . Example 1 Finding Lateral Area and Surface Area of Pyramids 1 2 1 2 . = +
The lateral area of a right pyramid is equal to one half the product of the perimeter of the base and the slant height. The surface area of a right pyramid is equal to the lateral area plus the base area.
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