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.

vectors_theorems07-00.jpg


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 {\dfrac 1 6}th of that of the parallelopiped. The expression can also be obtained using the following theorem :

vectors_theorems08-00.jpg

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s