In general, the surface area of a regular pyramid can be determined by finding the sum of the areas of the faces and the base.

Some pyramids have more than four faces.

 

Consider a right hexagonal pyramid:

  • The faces of the pyramid are made of 6 identical triangles, where b is the base of the triangles and s is height of the triangles (and the slant height of the pyramid).

  • The hexagonal base of the pyramid can be divided into 6 identical triangles, where b is the base of the triangles and a is the altitude of each triangle.

Recall that the formula for the area for a triangle is .


The formula for the surface area of a right hexagonal pyramid is



Key Lesson Marker


In general, the formula for the surface area of a right regular pyramid is

n is the number of identical faces of the pyramid (number of sides of the base)
s is the slant height of the pyramid
b is the length of one side of the base
a is the altitude of one triangle in the pyramid's base