Pyramidal Frustum

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid.

For a right pyramidal frustum, let be the slant height, the height, the bottom base perimeter, the top base perimeter, the bottom area, and the top area. Then the surface area (of the sides) and volume of a pyramidal frustum are given by

			(1)
			(2)

The geometric centroid of a right pyramidal frustum occurs at a height

(3)

above the bottom base (Harris and Stocker 1998).

The bases of a right -gonal frustum are regular polygons of side lengths and with circumradii

(4)

where is the side length, so the diagonal connecting corresponding vertices on top and bottom has length

(5)

and the edge length is

			(6)
			(7)

The triangular () and square () right pyramidal frustums therefore have side surface areas

			(8)
			(9)

The area of a regular -gon is

(10)

so the volumes of these frustums are

			(11)
			(12)

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