# Rectangular prism

A rectangular prism (also cuboid, rectangular box, right rectangular prism, rectangular paralleliped) is a three dimensional figure with 6 faces that are all rectangles.

Opposite faces of a rectangular prism are congruent and parallel.

The volume can be determined by multiplying the length, width, and height, $V = lwh$.

The length of the interior diagonals can be determined by using the formula $d = \sqrt{l^2 + w^2 + h^2}$.

Proof: To get a base diagonal, we use the pythagorean theorem: $\sqrt{l^2+w^2}$. We call that v. Then we use the pythagorean theorem again to get

• $diagonal=\sqrt{v^2+h^2}=\sqrt{l^2+w^2+h^2}$

• The surface area of the prism is $2lw+2wh+2lh$