The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry.


A pyramid is a geometric shape formed by connecting a polygonal face with a single point (the apex), thus creating n triangular faces (for a polygon of n vertices). At the left you see an oblique, quadrilateral pyramid and a right regular pentagonal pyramid.

There are only three kinds of pyramids which may have equilateral triangles: the tetrahedron, the square pyramid, and the pentagonal pyramid. All other pyramids don't have equilateral triangles. A right pyramid is a solid for which the line between the centroid C of the base polygon and the apex is perpendicular to the base.

The volume V of the pyramid is given by

V = Abh/3

with Ab being the area of the base polygon. For regular pyramids with n vertices of the base polygon, the volume V can be calculated as

with a being the length of a side of the base polygon.

Last Update: 2010-12-06