Frustum

If all its edges are forced to become of the same length, then a frustum becomes a prism (possibly oblique or/and with irregular bases).

Cones and pyramids can be viewed as degenerate cases of frusta, where one of the cutting planes passes through the apex (so that the corresponding base reduces to a point).

The formula for the volume of a pyramidal square frustum was introduced by the ancient Egyptian mathematics in what is called the Moscow Mathematical Papyrus, written in the 13th dynasty (c. 1850 BC): where a and b are the base and top side lengths, and h is the height.

The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus.

and substituting from its definition, the Heronian mean of areas B1 and B2 is obtained: the alternative formula is therefore: Heron of Alexandria is noted for deriving this formula, and with it, encountering the imaginary unit: the square root of negative one.