The perimeter of a hexagon is the total length of its outline. The perimeter of any figure can be calculated by adding the lengths of all the sides of the figure. In the case of a hexagon, we have six sides, so the perimeter is equal to the sum of the lengths of the six sides of the hexagon.

Here, we will look at more details about the perimeter of hexagons and we will learn about the formula that we can use. In addition, we will see some problems in which we will use the perimeter formula to obtain the answer.

## What is the formula to find the perimeter of a hexagon?

The perimeter of any geometric figure is found by adding the lengths of all the sides of the figure. We know that a hexagon has six sides, so its perimeter is:

$latex p=a+b+c+d+e+f$

where $latex a, ~ b, ~ c, ~ d, ~ e, ~ f$ are the six lengths of the sides of the hexagon.

In the case of regular hexagons, all six sides have the same length, so the perimeter is:

$latex p=6a$ |

where *a* is the length of one of the sides of the regular hexagon.

## Perimeter of a hexagon – Examples with answers

With the following examples, you can practice applying the formula for the perimeter of hexagons. It is recommended that you try to solve the exercises yourself before looking at the answer.

**EXAMPLE 1**

What is the perimeter of a hexagon that has sides of length 5 m?

##### Solution

We can use the perimeter formula with $latex a = 5$. Therefore, we have:

$latex p=6a$

$latex p=6(5)$

$latex p=30$

The perimeter of the hexagon is 30 m.

**EXAMPLE 2**

What is the perimeter of a hexagon that has sides of length 6 m?

##### Solution

We use the value $latex a=6$ in the perimeter formula. Therefore, we have:

$latex p=6a$

$latex p=6(6)$

$latex p=36$

The perimeter of the hexagon is 36 m.

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**EXAMPLE 3**

A hexagon has sides that are 13 cm long. What is the perimeter?

##### Solution

We have to use the perimeter formula with $latex a=13$. Therefore, we have:

$latex p=6a$

$latex p=6(13)$

$latex p=78$

The perimeter of the hexagon is 78 m.

**EXAMPLE 4**

A regular hexagon has a perimeter with a length of 72 m. What is the length of its sides?

##### Solution

In this case, we start with the perimeter and want to find the length of the sides of the hexagon. Therefore, we use the perimeter formula with $latex p=72$ and solve for *a*:

$latex p=6a$

$latex 72=6a$

$latex a=12$

The length of the sides is 12 m.

**EXAMPLE 5**

What is the length of the sides of a hexagon that has a perimeter of 126 m?

##### Solution

To find the length of the sides, we use the perimeter formula with $latex p=126$ and solve for *a*:

$latex p=6a$

$latex 126=6a$

$latex a=21$

The length of the sides is 21 m.

## Perimeter of a hexagon – Practice problems

Use the following problems to practice applying the formula for the perimeter of a hexagon. If you need help with these problems, you can look at the solved examples above.

## See also

Interested in learning more about hexagons? Take a look at these pages:

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