A **regular pyramid** is a pyramid whose base is a regular polygon and whose lateral edges are all equal in length. A pyramid is named by its base. Figure

Figure 1Some different types of regular pyramids.

The lateral faces of a regular pyramid are congruent isosceles triangles. The altitude of any of these triangles is the **slant height** of the regular pyramid. Figure 2

Figure 2A square pyramid.

Pyramids also have a lateral area, total area, and volume.

*Theorem 93*: The lateral area, *LA*, of a regular pyramid with slant height *l* and base perimeter *p* is given by the following equation.

**Example 1:** Find the lateral area of the square pyramid, shown in Figure 3

**Figure 3 **Finding the lateral area, total area, and volume of a square pyramid.

Because a pyramid has only one base, its total area is the sum of the lateral area and the area of its base.

*Theorem 94:* The total area, *TA*, of a regular pyramid with lateral area *LA* and base area *B* is given by the following equation.

**Example 2:** Find the total area of the regular pyramid shown in Figure

The base of the regular pyramid is a **square**. *A*_{square} = (side)^{2}. Therefore, *B* = 16^{2} in^{2}, or *B* = 256 in^{2}.

From the previous example,

*Theorem 95:* The volume, *V*, of a regular pyramid with base area *B* and altitude *h* is given by the following equation.

**Example 3:** Find the volume of the regular pyramid shown in Figure

From the previous example, *B* = 256 in^{2}. The figure indicates that *h* = 6 in.