A pyramid is a three-dimensional object with a polygon for a base and a triangular face coresponding to each side of the base. The triangular faces which are not the polygon base are called lateral faces and meet at a point called the vertex or apex.

A right pyramid is a pyramid that has its apex aligned directly above the center of the base.

Usually right pyramids with triangular bases, rectangular bases or bases which are regular polygons are studied. In the example below, the base is a regular pentagon.

In general, the volume of a pyramid is one-third the area of the base times the height of the pyramid.

In general, the surface area of a pyramid is the sum of the areas of all of the faces of the pyramid.

Right Pyramids with a Regular Polygon Base

a: The length of an apothem of the base of the pyramid

n: The number of sides of the base of the pyramid

s: The length of a side of the base of the pyramid

h: The height of the pyramid

V: The volume of the interior of the pyramid

S: The surface area of the pyramid

Explanation of volume formula (regular polygon base)

Explanation of surface area formula (regular polygon base)