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. Image Source : https://www.dune-project.org/ 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 th of that of the parallelopiped. The expression can also be obtained using the following theorem : Advertisements Share this:Click to share on Twitter (Opens in new window)Share on Facebook (Opens in new window)Click to share on Google+ (Opens in new window)Like this:Like Loading... Related