Perimeter of a pentagon

The perimeter, P, of a pentagon is the distance around its five straight sides.

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How you find the perimeter of a pentagon depends on what type of pentagon you have and what is known about it.


Regular and irregular pentagons

Regular pentagons have five congruent sides, five congruent interior angles, and five congruent exterior angles. Like all regular polygons, all the sides must be the same length, and all the angles must be the same measurement.

Irregular pentagons have five sides and five angles, but neither the sides nor the angles are congruent. An irregular polygon can have sides of five different lengths and angles of five different measures.

It is easier to find the perimeter of a regular pentagon since we have a formula. To find the perimeter of an irregular pentagon, you must measure and add up the five sides.

Perimeter of a pentagon formula

Using the perimeter of a pentagon formula, you can find the perimeter of a regular pentagon with relative ease. To find the perimeter of a regular pentagon with sides of length, s, you use this formula:


P = 5 × s

In our formula, 5 is the number of sides, and s is the length of the side that we know. Just like with the perimeter of a square, or the perimeter of a polygon in general, you find the perimeter of a pentagon by adding all the sides together.

If you are finding the perimeter of a regular pentagon, then you know that all five sides are equal lengths, so you can simplify the formula using multiplication instead of addition.

If you prefer to use the addition method your perimeter for a regular pentagon would look like this:

P = s + s + s + s + s

You have an s for each side of the pentagon.

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Perimeter of a regular pentagon example

Let"s pretend that we have a regular pentagon and that we know one side length is 3 cm. What is the perimeter of the pentagon?

If we know one side of a regular pentagon, then we know the length of each side because a regular pentagon has equal sides. We can simply plug our known side into our formula:

P = 5 × s

P = 5 × 3

P = 15

Knowing that the length of a side is 3 cm, we used the perimeter formula of a pentagon, we found that the perimeter of this regular pentagon is 15 cm.

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Another important part of a pentagon is the apothem and the area. Learn how to find the area of a pentagon using the area formula. You can find the area of a regular pentagon or an irregular pentagon.

Next Lesson:

Area of a Pentagon


What you learned:

After working your way through this lesson, you should know:

How to find the perimeter of a pentagonThe difference between regular and irregular pentagonsHow to use the perimeter of a pentagon formula to find the perimeter of a regular pentagon