Subject: Geometry
Name: Hai Van
Who are you: Parent

Could you please show me the way to calculate the volume of an irregular tetrahedron (I.e. how to find the volume of a tetrahedron given the lengths of its sides) ?

I've spent a lot of time to find the solution on the net and got no result. Pls kindly help me as soon as you can.

Thanks and best regards.

Hai Van


Hai Van,

There is an expression for the volume of a tetrahedron on the MathWorld site. Label the vertices of the tetrahedron 1, 2, 3 and 4, let dij be the length of the edge from vertex i to vertex j and let V be the volume of the tetrahedron then the MathWorld expression is the determinant equation

tetrahedron volume

If you can find the height of the tetrahedron then you can use a much simpler expression.

volume = 1/3 x (area of the base) x height

The area of the base can be found using Heron's Formula.