When calculating the volume of a pyramid we can consider a pyramid to any 3D shape with a base of a regular polygon (or circle, in which case the resulting shape is a cone) that then goes to a point as shown below.

Pyramids with different base shapes

The volume, V, of any of these pyramids is given by a third of base area, A, multiplied by the height, h or can be written as

V=Ah/3

The most usual way to prove this is to split the pyramid up into layers which can be approximated as cuboids, then by increasing the number of layers and therefore reducing the thickness of each layer the approximation becomes better untill when the the width of each layer tends to zero you get the exact volume of the pyramid.

To see an actual proof see

http://www.trans4mind.com/personal_development/mathematics/geometry/pyramids.htm