frustum of a pyramid

Certain ancient Native American mounds also form the frustum of a pyramid.

The Heronian mean may be used in finding the volume of a frustum of a pyramid or cone.

Problem 14 in the Moscow Mathematical Papyrus gives the only ancient example finding the volume of a frustum of a pyramid, describing the correct formula:

The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid.

However, the words 'representation of the frustum of a pyramid upside down, with a rectangular base area approximately 25 cm x 8 cm and bevelled lateral faces' appear under the heading 'Specification of the other type of trade mark' in theapplication form.

For the volume of a frustum of a pyramid, he gives the "pragmatic" value as the depth times the square of the mean of the edges of the top and bottom faces, and he gives the "superficial" volume as the depth times their mean area.