11-3 Surface Areas of Pyramids and Cones

Objective

To find the surface area of a pyramid and a cone

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The Solve It involves the triangular faces of a roof and the three-dimensional figures they form. In this lesson, you will learn to name such figures and to use formulas to find their areas.

Essential Understanding To find the surface area of a three-dimensional figure, find the sum of the areas of all the surfaces of the figure.

A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex (called the vertex of the pyramid).

Hexagonal pyramid

You name a pyramid by the shape of its base. The altitude of a pyramid is the perpendicular segment from the vertex to the plane of the base. The length of the altitude is the height h of the pyramid.

Square pyramid

A regular pyramid is a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. The slant height l is the length of the altitude of a lateral face of the pyramid.

In this book, you can assume that a pyramid is regular unless stated otherwise.

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