Perimeter of Pentagon
2026-02-28 10:03 Diff
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Last updated on September 26, 2025

The perimeter of a shape is the total length of its boundary. The sum of all five sides is called the perimeter of a pentagon. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a pentagon.

What is the Perimeter of a Pentagon?

The perimeter of a pentagon is the total length of its five sides. By adding the length of all five sides, we get the perimeter of the shape.

The formula for the perimeter of a pentagon is 𝑷 = 𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒, where a, b, c, d, and e are the sides of the pentagon. For instance, if a pentagon has sides, a = 5, b = 7, c = 6, d = 9, and e = 4, then its perimeter is p = 5 + 7 + 6 + 9 + 4 = 31.

Formula for Perimeter of Pentagon - 𝑷 = 𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒.

Let’s consider another example of a pentagon with side lengths, 𝑎 = 11, 𝑏 = 8, 𝑐 = 10, 𝑑 = 7, and 𝑒 = 9.

So the perimeter of the pentagon will be: 𝑷 = 𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒 = 11 + 8 + 10 + 7 + 9 = 45.

How to Calculate the Perimeter of Pentagon

To find the perimeter of a pentagon, we just need to apply the given formula and sum all the sides of the pentagon. For instance, a given pentagon has the sides of a = 6, b = 5, c = 5, d = 6, and e = 8. Perimeter = sum of all sides = 6 + 5 + 5 + 6 + 8 = 30 cm.

Example Problem on Perimeter of Pentagon

For finding the perimeter of a pentagon, we use the formula, 𝑷 = 𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒.

For example, let’s say, a = 7 cm, b = 9 cm, c = 4 cm, d = 5 cm, and e = 6 cm.

Now, the perimeter = sum of all sides = 7 + 9 + 4 + 5 + 6 = 31 cm.

Therefore, the perimeter of the pentagon is 31 cm.

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Tips and Tricks for Perimeter of Pentagon

Learning some tips and tricks makes it easier for children to calculate the perimeter of pentagons. Here are some tips and tricks given below: Always remember that a pentagon's perimeter is simply the sum of the five sides of the shape.

For that, use the formula, 𝑷 = 𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒. Calculating the perimeter of a pentagon starts by determining the length of each side using the distance formula. The distance formula is: Distance = √((x2-x1)² + (y2-y1)²). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make up a pentagon’s side.

They can be found by adding the lengths of five sides after they are calculated. To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of pentagons. After that, apply the formula to each pentagon.

To avoid mistakes when adding the perimeter, make sure the side lengths are precise and constant for common uses like gardening and architecture. If you are given the semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. Area-related calculations often use the semi-perimeter.

Common Mistakes and How to Avoid Them in Perimeter of Pentagon

Did you know that while working with the perimeter of a pentagon, children might encounter some errors or difficulties?

We have many solutions to resolve these problems. Here are some given below:

Problem 1

A garden plot is shaped like a pentagon and has a perimeter of 60 meters. Four sides measure 12 meters each. To find out the missing side, subtract the sum of the known sides from the total perimeter.

Okay, lets begin

Length of the missing side = 12 meters.

Explanation

Let ‘e’ be the side of the missing side. And the given perimeter = 60 meters.

Length of the four equal sides = 12 meters.

Perimeter of pentagon = sum of lengths of five sides.

60 = 12 + 12 + 12 + 12 + e 60 = 48 + e e = 60 – 48 = 12 e = 12

Therefore, the missing side is 12 meters.

Well explained 👍

Problem 2

A wire with a perimeter of 100 inches is reshaped into a regular pentagon. Find the length of each side of the pentagon and divide the total length by 5.

Okay, lets begin

20 inches

Explanation

Given that the perimeter of a wire is reshaped into a regular pentagon, here is the solution:

Perimeter of the wire = Total length of the wire

Length of the wire used = Perimeter of the pentagon formed

Perimeter of a regular pentagon = 5 × a 100 = 5 × a 100 ÷ 5 = 20 a = 20

Therefore, the length of each side of the pentagon is 20 inches.

Well explained 👍

Problem 3

Find the perimeter of a regular pentagon whose sides are 8 cm.

Okay, lets begin

40 cm

Explanation

Perimeter of pentagon = a + b + c + d + e P = 8 + 8 + 8 + 8 + 8 = 40

Therefore, the perimeter of the pentagon is 40 cm.

Well explained 👍

Problem 4

Emma is planning a pentagon-shaped flower bed in her backyard. She measures the five sides of the bed: Side A = 10 meters Side B = 8 meters Side C = 12 meters Side D = 9 meters Side E = 11 meters How much fencing should Emma buy to go around the edge of the flower bed?

Okay, lets begin

Emma will need 50 meters of fencing to go around the flower bed.

Explanation

The perimeter of a pentagon is the sum of all the five sides.

Using the formula: P = a + b + c + d + e P = 10 + 8 + 12 + 9 + 11 = 50 meters.

Well explained 👍

Problem 5

Find the perimeter of an irregular pentagon with side lengths a = 14, b = 10, c = 9, d = 8, and e = 13 meters.

Okay, lets begin

Perimeter = a + b + c + d + e = 14 + 10 + 9 + 8 + 13 = 54 meters.

Explanation

Each side of the irregular pentagon has a different length.

The entire distance is calculated around the pentagon to be 54 meters by summing the lengths of the five sides.

Well explained 👍

FAQs on Perimeter of Pentagon

1.Evaluate the pentagon’s perimeter if its sides are 5 cm, 7 cm, 6 cm, 8 cm, and 9 cm.

Perimeter of pentagon = a + b + c + d + e, Hence P = 5 + 7 + 6 + 8 + 9 = 35 cm.

2.What is meant by a pentagon’s perimeter?

The total length around a pentagon’s sides is its perimeter. In other words, the perimeter of a pentagon is the total length of its sides.

3.What are the types of pentagons?

There are two main types of pentagons: Regular pentagon, where all sides and angles are equal, and Irregular pentagon, where the sides and angles are not equal.

4.Which pentagon has no equal sides?

An irregular pentagon is a pentagon with no equal sides. All five sides of the irregular pentagon are different.

5.What is a regular pentagon?

A regular pentagon is a five-sided polygon where all sides and angles are equal.

Important Glossaries for Perimeter of Pentagon

  • Perimeter: The total length of the sides of a shape.
  • Pentagon: A polygon with five sides and five angles.
  • Regular Pentagon: A pentagon with all equal sides and angles.
  • Irregular Pentagon: A pentagon with sides and angles of different lengths.
  • Formula of perimeter for a pentagon: The mathematical expression used to calculate the perimeter of a pentagon is 𝑷 = 𝑎 + 𝑏 + 𝑐 + 𝑑 + 𝑒.

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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

Fun Fact

: She has songs for each table which helps her to remember the tables