### Find the volume of an irregular tetrahedron form its edges:

Suppose you are given the 6 sides of an irregular tetrahedron and you need to find the volume consumed by it.

Let the given sides to be u, v, w, W, V, U. Here,

Let:

u′ = v² + w² - U²

v′ = w² + u² - V²

w′ = u² + v² - W²

Now:

volume =

This formula is derived from the determinant which can be found here for more reading. As the formula is symmetric, the ordering of the pairs won't make any change to the formula.

Read more properties about Tetrahedrons from Wikipedia.

**(u, U), (v, V), (w, W)**are considered to be opposite edge pairs ( opposite edges means the edges which do not share common vertices ). Now the volume can be found from the following formula:Let:

u′ = v² + w² - U²

v′ = w² + u² - V²

w′ = u² + v² - W²

Now:

volume =

^{1}⁄_{12}× √(4u²v²w² - u²u′² - v²v′² - w²w′² + u′v′w′)This formula is derived from the determinant which can be found here for more reading. As the formula is symmetric, the ordering of the pairs won't make any change to the formula.

Read more properties about Tetrahedrons from Wikipedia.