Volume of a Prism (regular polygon base)
Formula

a: The length of an apothem of the base of the prism

n: The number of sides of the base of the prism

s: The length of a side of the base of the prism

h: The height of the prism


V: The volume of the prism

Volume of a prism

Explanation

In general, the volume of a prism is the area of the base times the height of the prism.

Volume of a prism formula

The area of a regular polygon is given by the formula below:

Area of a regular polygon formula

Substitute to get the following:

Substitution

Simplify to get the final result:

Volume of a prism