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100 LearnersLast updated on September 8, 2025
Perimeter of Regular Octagon
The perimeter of a shape is the total length of its boundary. In a regular octagon, all sides are equal, and the perimeter is the sum of these eight equal sides. Perimeter calculations are useful for various applications such as construction, design, and more. In this topic, we will learn about the perimeter of a regular octagon.
What is the Perimeter of a Regular Octagon?
The perimeter of a regular octagon is the total length of its eight equal sides. By multiplying the length of one side by eight, 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.
For instance, if a regular octagon has a side length of 5, then its perimeter is P = 8 × 5 = 40.
Formula for Perimeter of Regular Octagon - 𝑷 = 8 × 𝑎.
Let’s consider another example of a regular octagon with a side length of 7. So the perimeter of the octagon will be: 𝑷 = 8 × 𝑎 = 8 × 7 = 56.
How to Calculate the Perimeter of a Regular Octagon
To find the perimeter of a regular octagon, apply the given formula by multiplying the length of one side by eight.
For instance, if a regular octagon has a side length of 4, the perimeter = 8 × 4 = 32 cm.
Example Problem on Perimeter of Regular Octagon -
For finding the perimeter of a regular octagon, use the formula, 𝑷 = 8 × 𝑎.
For example, let’s say, a = 6 cm. Now, the perimeter = 8 × 6 = 48 cm.
Therefore, the perimeter of the regular octagon is 48 cm.
Tips and Tricks for Perimeter of Regular Octagon
Learning some tips and tricks makes it easier for children to calculate the perimeter of regular octagons. Here are some tips and tricks given below:
- Always remember that a regular octagon's perimeter is simply eight times the length of one side. Use the formula, 𝑷 = 8 × 𝑎.
- If given the total perimeter of a regular octagon, divide it by 8 to find the length of one side.
- If you have a complex figure composed of a regular octagon and other shapes, calculate the octagon's perimeter separately and add it to the perimeters of the other shapes.
- When measuring the sides for accurate construction or design, ensure all sides are equal to avoid errors in the perimeter calculation.
- For practical applications like tiling or creating frames, ensure the calculated perimeter matches the available materials to prevent shortages or excess.
Common Mistakes and How to Avoid Them in Perimeter of Regular Octagon
Did you know that while working with the perimeter of a regular octagon, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Miscounting the number of sides of the octagon.
Always remember that a regular octagon has eight sides. Ensure each side is counted to apply the formula correctly.
Mistake 2
Confusing the concept of area with perimeter, leading to incorrect calculations.
It is important to note that the perimeter, calculated in linear units, is the total length around the octagon, while the area, in square units, represents the space inside the octagon.
Mistake 3
Using incorrect values for the side length, misreading a problem, or mislabeling the sides.
Double-check the problem and ensure that you're using the correct side length for your octagon.
Mistake 4
Misunderstanding or misidentifying the side length given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if possible, verify the figure to accurately identify the side length.
Mistake 5
Assuming irregular octagon calculations apply to regular octagons.
Regular octagons have equal sides, so use the formula 𝑷 = 8 × 𝑎 for accurate calculations.
Perimeter of Regular Octagon Examples
Problem 1
A stop sign is shaped like a regular octagon and has a perimeter of 64 inches. What is the length of one side of the sign?
Length of one side = 8 inches.
Explanation
Let ‘a’ be the length of one side of the octagon. And the given perimeter = 64 inches. Perimeter of regular octagon = 8 × a 64 = 8 × a a = 64 ÷ 8 = 8
Therefore, the length of one side is 8 inches.
Problem 2
A garden is designed in the shape of a regular octagon with each side measuring 12 meters. What is the total fencing required around the garden?
96 meters
Explanation
Given that each side of the regular octagon is 12 meters.
Perimeter of the octagon = 8 × a Perimeter = 8 × 12 = 96 meters
Therefore, the total fencing required is 96 meters.
Problem 3
Find the perimeter of a regular octagon with a side length of 9 cm.
72 cm
Explanation
Perimeter of regular octagon = 8 × a P = 8 × 9 = 72
Therefore, the perimeter of the regular octagon is 72 cm.
Problem 4
A decorative tile is in the shape of a regular octagon. If the perimeter of the tile is 80 cm, find the length of each side.
10 cm
Explanation
The perimeter of a regular octagon is the sum of all eight equal sides.
Using the formula: P = 8 × a 80 = 8 × a a = 80 ÷ 8 = 10 cm
Therefore, the length of each side of the tile is 10 cm.
Problem 5
A tabletop is shaped like a regular octagon. Each side measures 15 inches. What is the perimeter of the tabletop?
Perimeter = 8 × 15 = 120 inches.
Explanation
Each side of the regular octagon is equal, and the entire distance around the tabletop is calculated by multiplying one side's length by eight. Therefore, the perimeter is 120 inches.
FAQs on Perimeter of Regular Octagon
1.Evaluate the octagon’s perimeter if its side length is 11 cm.
2.What is meant by a regular octagon’s perimeter?
3.How many sides does a regular octagon have?
4.What is a regular octagon?
5.What shape has the maximum number of equal sides that can form a regular polygon?
Important Glossaries for Perimeter of Regular Octagon
- Perimeter: The total length of the sides of a shape.
- Regular Octagon: A polygon with eight equal sides and eight equal angles.
- Formula of Perimeter: The mathematical expression used to calculate the perimeter of a regular octagon is 𝑷 = 8 × 𝑎.
- Side Length: The length of one side of a polygon.
- Polygon: A closed plane figure with multiple straight sides.
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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
