# 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:

### Related items

#### Euler's polyhedron formula

The theorem formulated by Leonhard Euler describes one of the basic properties of convex polyhedra.

#### Ratio of volumes of similar solids

This 3D scene explains the correlation between the ratio of similarity and the ratio of volume of geometric solids.

#### Regular square pyramid

A regular square pyramid is a right pyramid with a square base and four triangular faces.

#### Volume of spheres (Cavalieri´s principle)

Calculating the volume of a sphere is possible using an appropriate cylinder and cone.

#### Volume of spheres (demonstration)

The sum of the volume of the ´tetrahedrons´ gives an approximation of the volume of the sphere.

#### Platonic solids

This animation demonstrates the five regular three-dimensional (or Platonic) solids, the best known of which is the cube.

#### Szilassi polyhedron

This special concave polyhedron was named after a Hungarian mathematician.

#### Grouping of solids 1

This animation demonstrates various groups of solids through examples.

#### Grouping of solids 2

This animation demonstrates various groups of solids through examples.

#### Grouping of solids 3

This animation demonstrates various groups of solids through examples.

#### Grouping of solids 4

This animation demonstrates various groups of solids through examples.