117 LearnersLast updated on August 5th, 2025
Perimeter of Octagon
The perimeter of a shape is the total length of its boundary. The sum of all eight sides is called the perimeter of an octagon. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of an octagon.
What is the Perimeter of an Octagon?
The perimeter of an octagon is the total length of its eight sides. By adding the length of all eight sides, we get the perimeter of the shape. The formula for the perimeter of a regular octagon is 𝑃 = 8 × 𝑎, where 𝑎 is the length of one side of the octagon. For instance, if an octagon has equal sides each measuring 6 units, then its perimeter is 𝑃 = 8 × 6 = 48 units.
Formula for Perimeter of Octagon - 𝑃 = 8 × 𝑎 for a regular octagon.
Let’s consider another example of a regular octagon with side lengths, 𝑎 = 10 units. So the perimeter of the octagon will be: 𝑃 = 8 × 𝑎 = 8 × 10 = 80 units.
How to Calculate the Perimeter of an Octagon
To find the perimeter of a regular octagon, we just need to apply the given formula and multiply the length of one side by eight. For instance, a regular octagon has sides of length 7 units. Perimeter = 8 × side length = 8 × 7 = 56 units. Example Problem on Perimeter of Octagon - For finding the perimeter of a regular octagon, we use the formula, 𝑃 = 8 × 𝑎. For example, let’s say, each side 𝑎 = 9 cm. Now, the perimeter = 8 × 9 = 72 cm. Therefore, the perimeter of the octagon is 72 cm.
Tips and Tricks for Perimeter of Octagon
Learning some tips and tricks makes it easier for children to calculate the perimeter of octagons. Here are some tips and tricks given below: Always remember that a regular octagon's perimeter is simply 8 times the length of one side of the shape. For that, use the formula, 𝑃 = 8 × 𝑎. Calculating the perimeter of an irregular octagon starts by determining the length of each side. Then, sum all the side lengths to find the perimeter. To reduce confusion, specifically, arrange the indicated side lengths if you need the perimeter of a group of octagons. After that, apply the appropriate formula to each octagon. To avoid mistakes when adding the perimeter, make sure the side lengths are precise and consistent 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.
Common Mistakes and How to Avoid Them in Perimeter of Octagon
Did you know that while working with the perimeter of an octagon, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly assuming all octagons have equal sides.
Remember that only regular octagons have equal sides. For irregular octagons, the lengths of all the sides should be summed up individually to find the perimeter.
Mistake 2
Students may confuse the concepts of area and perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length of the octagon’s sides, while the area, in square units, represents the space inside the octagon.
Mistake 3
Assuming that every octagon is regular, which results in inaccurate calculations.
Irregular octagons have sides of different lengths. Always be careful about the type of octagon to ensure accurate calculations.
Mistake 4
Using the wrong values for the length of the sides, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct lengths for your octagon.
Mistake 5
Misunderstanding or misidentifying the side lengths that are given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if it's possible, try to draw the octagon to accurately identify the side lengths.
Perimeter of Octagon Examples
Problem 1
A regular octagonal-shaped garden has a perimeter of 64 meters and all sides are equal. What is the length of one side of the garden?
Length of one side = 8 meters.
Explanation
Let ‘a’ be the length of one side. And the given perimeter = 64 meters. Perimeter of regular octagon = 8 × a 64 = 8 × a a = 64 ÷ 8 = 8 Therefore, the length of one side is 8 meters.
Problem 2
A piece of wire with a total length of 160 inches is reshaped into a regular octagon. Find the length of each side of the octagon.
20 inches
Explanation
Given that the total length of the wire is equal to the perimeter of the octagon, here is the solution: Perimeter of the octagon = Total length of the wire Perimeter of a regular octagon = 8 × a 160 = 8 × a 160 ÷ 8 = 20 a = 20 Therefore, the length of each side of the octagon is 20 inches.
Problem 3
Find the perimeter of a regular octagon whose sides are each 15 cm.
120 cm
Explanation
Perimeter of octagon = 8 × a P = 8 × 15 = 120 Therefore, the perimeter of the octagon is 120 cm.
Problem 4
Jamie is planning an octagonal flower bed in her backyard. She measures the length of each side of the bed to be 5 meters. How much fencing should Jamie buy to go around the edge of the bed?
Jamie will need 40 meters of fencing to go around the bed.
Explanation
The perimeter of a regular octagon is the sum of all the eight sides. Using the formula: P = 8 × a P = 8 × 5 = 40 meters.
Problem 5
A stop sign is in the shape of a regular octagon with each side measuring 12 inches. Find the perimeter of the sign.
Perimeter = 8 × 12 = 96 inches.
Explanation
Each side of the regular octagon is equal. The entire distance around the stop sign is calculated to be 96 inches by multiplying the length of one side by eight.
FAQs on Perimeter of Octagon
1.Evaluate the octagon’s perimeter if each of its sides is 7cm.
2.What is meant by an octagon’s perimeter?
3.What are the types of octagons?
4.Which octagon has all equal sides?
5.Which type of octagon can have different side lengths?
Important Glossaries for Perimeter of Octagon
Perimeter: The total length of the sides of a shape. Octagon: A polygon with eight sides and eight angles. Regular Octagon: An octagon where all sides and angles are equal. Irregular Octagon: An octagon with sides and angles of different lengths and measures. Formula for Perimeter: The mathematical expression used to calculate the perimeter of a regular octagon is 𝑃 = 8 × 𝑎.
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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
