Volume of a tetrahedron

Volume of a tetrahedron

To calculate the volume of a tetrahedron we start by calculating the volume of a prism.

Mathematics

Keywords

Volume of the tetrahedron, tetrahedron, Volume of a triangular pyramid, volume, prism, The volume of a pyramid, geometry, mathematics

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Scenes

To calculate the volume of a tetrahedron we shall start with a triangular prism, since we already know how to calculate its volume, i.e. the base area multiplied by the height:

It is easy to note that a triangular prism can be segmented into three tetrahedrons. This is demonstrated in the animation.

Cavalieri's principle, which we are already familiar with, is valid for any two of the three tetrahedra resulting from the division of the triangular prism.

This is illustrated in the animation by pressing the '<<<' and '>>>' buttons.

This means that the volumes of the three tetrahedra are identical. As their sum represents the volume of the prism, we can conclude that to obtain the volume of the tetrahedron ABCD we need the third of the volume of the prism according to the following formula:

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