Volume of a Triangular Pyramid (Tetrahedron)
The illustration here shows how a triangular prism (tetrahedron) can be cut into three triangular pyramids, each having the same volume. The drawing is based on Euclid's Proposition 7 from Book XII. It follows that the volume of one such pyramid is 1/3 of the volume of the prism with a base and altitude in common with the pyramid.
You can view Euclid's proof online: Book XII Proposition 7
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Date last modified: April 10, 2009.