120 LearnersLast updated on August 5th, 2025
Perimeter of Regular Polygon
The perimeter of a shape is the total length of its boundary. For a regular polygon, the perimeter is the sum of the lengths of all its equal sides. Perimeter is used in various applications such as fencing, sewing, and more. In this topic, we will learn about the perimeter of a regular polygon.
What is the Perimeter of a Regular Polygon?
The perimeter of a regular polygon is the total length of all its sides. Since all sides of a regular polygon are equal, the perimeter can be calculated by multiplying the length of one side by the total number of sides. The formula for the perimeter of a regular polygon is π = π Γ π , where n is the number of sides, and s is the length of each side. For instance, if a regular hexagon has a side length of 6, with 6 sides, then its perimeter is π = 6 Γ 6 = 36.
Formula for Perimeter of Regular Polygon - π = π Γ π
Letβs consider another example of a regular octagon with side length 8. So the perimeter of the octagon will be: π = π Γ π = 8 Γ 8 = 64.
How to Calculate the Perimeter of a Regular Polygon
To find the perimeter of a regular polygon, use the formula and multiply the length of one side by the number of sides. For instance, a given regular pentagon has a side length of 5. Perimeter = number of sides Γ length of one side = 5 Γ 5 = 25 cm. Example Problem on Perimeter of Regular Polygon - To find the perimeter of a regular polygon, use the formula π = π Γ π . For example, letβs say a regular decagon has a side length of 4 cm. Now, the perimeter = 10 Γ 4 = 40 cm. Therefore, the perimeter of the decagon is 40 cm.
Tips and Tricks for Perimeter of Regular Polygon
Here are some tips and tricks to easily calculate the perimeter of regular polygons: Always remember that a regular polygon's perimeter is simply the number of sides times the length of one side. Use the formula π = π Γ π . When given the side length and the number of sides, directly apply the formula to get the perimeter. For calculations involving regular polygons, ensure the side lengths are precise, especially in practical applications like architecture. If the semi-perimeter (half the perimeter) is given, multiply it by 2 to find the full perimeter. This concept is useful for various geometrical calculations.
Common Mistakes and How to Avoid Them in Perimeter of Regular Polygon
While calculating the perimeter of a regular polygon, some errors or difficulties may arise. Here are solutions to avoid these problems:
Mistake 1
Confusing the perimeter formula with area formulas for polygons.
Remember that the perimeter involves linear measurements (length), and the formula is π = π Γ π , whereas area calculations involve square units.
Mistake 2
Assuming all polygons are regular, leading to incorrect calculations.
Only regular polygons have equal sides. Ensure the polygon is regular before applying the perimeter formula.
Mistake 3
Using wrong side lengths or miscounting the number of sides in a polygon.
Double-check the number of sides and ensure the correct side length is used in the formula.
Mistake 4
Misinterpreting problem statements or diagrams.
Carefully read the problem or examine diagrams to correctly identify the number of sides and side lengths.
Perimeter of Regular Polygon Examples
Problem 1
A regular hexagonal tile has a side length of 12 inches. Calculate the perimeter of the tile.
72 inches
Explanation
Given side length = 12 inches, and the hexagon has 6 sides. Perimeter of hexagon = number of sides Γ side length = 6 Γ 12 = 72 inches.
Problem 2
A gardener is designing a regular pentagonal flower bed with each side measuring 5 feet. Find the perimeter of the flower bed.
25 feet
Explanation
Given side length = 5 feet, and the pentagon has 5 sides. Perimeter of pentagon = number of sides Γ side length = 5 Γ 5 = 25 feet.
Problem 3
A regular octagonal stop sign has a side length of 10 cm. What is the perimeter of the stop sign?
80 cm
Explanation
Perimeter of octagon = number of sides Γ side length = 8 Γ 10 = 80 cm.
Problem 4
A regular heptagonal garden has each side measuring 7 meters. How much fencing is required to enclose the garden?
49 meters
Explanation
The perimeter of a heptagon is the sum of all its sides. Using the formula: π = π Γ π = 7 Γ 7 = 49 meters.
Problem 5
Calculate the perimeter of a regular dodecagon with each side measuring 3 inches.
36 inches
Explanation
Each side of the dodecagon is equal. The perimeter is calculated by summing the lengths of the 12 sides. π = 12 Γ 3 = 36 inches.
FAQs on Perimeter of Regular Polygon
1.Evaluate the perimeter of a regular hexagon with a side length of 7 cm.
2.What is meant by a regular polygon's perimeter?
3.What are the types of polygons?
4.Which polygon has no equal sides?
5.Which polygon has the smallest perimeter for a given area?
Important Glossaries for Perimeter of Regular Polygon
Perimeter: The total length of the sides of a shape. Regular Polygon: A polygon with all sides and angles equal. Formula of Perimeter: The mathematical expression used to calculate the perimeter of a regular polygon is π = π Γ π . Side Length: The length of one side of a polygon. Number of Sides: The total count of sides in a polygon.
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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
