## Volume of Parallelopiped and Tetrahedron

A parallelopiped is a 3-D object, each of whose faces is a parallelogram.

A rectangular parallelopiped is the one, whose faces are rectangular.

A cube is a rectangular parallelopiped, whose edges are of equal length.

A tetrahedron is a 3-D object, whose all faces are triangular. It can be shown that a parallelopiped can be decomposed into 6 tetrahedra.

For a visual proof :  1 Parallelopipded  = 6 Tetrahedra

Let there be 2 such objects, whose coterminus edges are identical. Then, the volume of the tetrahedron is ${\dfrac 1 6}$th of that of the parallelopiped. The expression can also be obtained using the following theorem :