# Perimeter of a Pentagon – Formulas and Examples

The perimeter of a pentagon is given by the total length of the outline of the pentagon. This means that we can calculate its perimeter by adding the lengths of all its sides. When we have a regular pentagon, all the sides are equal, so we simply need the length of one of the sides of the pentagon to calculate the perimeter.

Here, we will learn about the formula that we can use to calculate the perimeter of a regular pentagon. In addition, we will look at some problems in which we will apply this formula to find the answer.

##### GEOMETRY

Relevant for

Learning about the perimeter of a pentagon with examples.

See examples

##### GEOMETRY

Relevant for

Learning about the perimeter of a pentagon with examples.

See examples

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

The perimeter of a pentagon is the total length of the pentagon’s boundaries. Therefore, we can find the perimeter by adding the lengths of the five sides of the pentagon:

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

where, $latex a, ~ b, ~ c, ~ d, ~ e$ represent the lengths of the sides of the pentagon. In the case of regular pentagons, all sides have the same length, so the perimeter formula becomes:

where a is the length of one of the sides of the pentagon.

## Perimeter of a pentagon – Examples with answers

With the following examples, you can practice using the formula for the perimeter of the pentagon. Each example has its respective solution, but it is recommended that you try to solve the exercises yourself before looking at the answer.

### EXAMPLE 1

What is the perimeter of a pentagon that has sides of length 10 m?

We use the perimeter formula using the value $latex a=10$. Therefore, we have:

$latex p=5a$

$latex p=5(10)$

$latex p=50$

The perimeter of the pentagon is 50 m.

### EXAMPLE 2

What is the perimeter of a pentagon that has sides of length 11 m?

We plug the value $latex a=11$ into the perimeter formula. Therefore, we have:

$latex p=5a$

$latex p=5(11)$

$latex p=55$

The perimeter of the pentagon is 55 m.

### EXAMPLE 3

A pentagon has sides that are 15 m long. What is its perimeter?

From the question, we have the value $latex a=15$. Therefore, we use the perimeter formula with this value:

$latex p=5a$

$latex p=5(15)$

$latex p=75$

The perimeter of the pentagon is 75 m.

### EXAMPLE 4

The perimeter of a pentagon is equal to 20 m. What is the length of one of its sides?

In this case, we start with the perimeter and want to find the length of one of the sides. Therefore, we have to use the perimeter formula and solve for a:

$latex p=5a$

$latex 20=5a$

$latex a=4$

The length of one side of the pentagon is 4 m.

### EXAMPLE 5

The perimeter of a pentagon is equal to 105 cm. What is the length of one of its sides?

We have to use the perimeter formula and solve for a. Using the value $latex p= 105$, we have:

$latex p=5a$

$latex 105=5a$

$latex a=21$

The length of one of the sides is 21 cm.

## Perimeter of a pentagon – Practice problems

Use the formula for the perimeter of pentagons to solve the following problems. If you need help with this, you can look at the solved examples above.

#### A pentagon has a perimeter of 85m. What is the length of its sides?  