Geometry

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# Volume of a Hexagonal Prism

#### Lesson Contents

## Hexagonal Prism Volume Formula

The formula for volume of a hexagonal prism is given as:**V = ^{3√3}⁄_{2}a^{2}h**

Where

*V*is the volume,

*a*is the hexagon base’s edge length, and

*h*is the height of the prism.

### What is a Hexagonal Prism?

A hexagonal prism is the three-dimensional shape that is created from extending the face of a hexagon upwards into the third dimension. Since a hexagon is two dimensional, it becomes a prism once it extends upwards into the third dimension.

The difference between a hexagonal prism and a rectangular prism is the shape of the cross section. The cross section of a prism is what we see if we cut the prism on a plane that is parallel to its base plane. It will appear as the shape that the base of the prism is made of, which is a hexagon in the case of a hexagonal prism, and a rectangle in the case of a rectangular prism.

### Example Problem

Find the volume of a hexagonal prism with a base edge length of 20 and a prism height of 10.

Solution:

1.) We have all values needed to use the volume formula directly. Let’s plug the given dimensions into the volume formula.

2.) V = ^{3√3}⁄_{2}a^{2}h

V = ^{3√3}⁄_{2}(20^{2})(10) = 10,392.3

3.) **The volume of the hexagonal prism is 10,392.3.**