105 LearnersLast updated on July 29th, 2025
Perimeter of Polygon
The perimeter of a shape is the total length of its boundary. The sum of all the sides is called the perimeter of a polygon. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of a polygon.
What is the Perimeter of a Polygon?
The perimeter of a polygon is the total length of its sides. By adding the length of all sides, we get the perimeter of the shape. The formula for the perimeter of a polygon depends on the number of sides. For instance, if a pentagon has sides of lengths 5, 7, 8, 6, and 4, then its perimeter is P = 5 + 7 + 8 + 6 + 4 = 30.
Formula for Perimeter of Polygon
Let’s consider another example of a hexagon with sides of lengths 3, 5, 6, 7, 4, and 2. So the perimeter of the hexagon will be: P = 3 + 5 + 6 + 7 + 4 + 2 = 27.
How to Calculate the Perimeter of a Polygon
To find the perimeter of a polygon, we just need to apply the given formula and sum all the sides of the polygon. For instance, a given octagon has sides of lengths 4, 4, 4, 4, 4, 4, 4, and 4. Perimeter = sum of all sides = 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32 units. Example Problem on Perimeter of Polygon - For finding the perimeter of a polygon, we use the formula, P = sum of all sides. For example, let’s say a quadrilateral has sides: 5 cm, 4 cm, 3 cm, and 2 cm. Now, the perimeter = sum of all sides = 5 + 4 + 3 + 2 = 14 cm. Therefore, the perimeter of the quadrilateral is 14 cm.
Tips and Tricks for Perimeter of Polygon
Learning some tips and tricks makes it easier for children to calculate the perimeter of polygons. Here are some tips and tricks given below: Always remember that a polygon's perimeter is simply the sum of the sides of the shape. For that, use the formula, P = sum of all sides. Calculating the perimeter of a polygon 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 polygon’s side. They can be found by adding the lengths of all sides after they are calculated. To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of polygons. After that, apply the formula to each polygon. 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, like Heron’s formula, often use the semi-perimeter.
Common Mistakes and How to Avoid Them in Perimeter of Polygon
Did you know that while working with the perimeter of a polygon, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using the Pythagorean theorem (a² + b² = c²) for polygons that do not form right-angled triangles.
Remember that only right-angled triangles can use the Pythagorean theorem. The lengths of all the sides of other polygon types should be summed up 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 polygon’s sides, while the area, in square units, represents the space inside the polygon.
Mistake 3
Assuming that every polygon has equal sides, which results in inaccurate calculations.
A scalene polygon has all sides of different lengths. Always be careful about the type of polygon 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 polygon.
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 polygon to accurately identify the side lengths.
Perimeter of Polygon Examples
Problem 1
A pentagon-shaped garden has a perimeter of 60 meters, and four sides measure 12 meters each. To find out the missing side of the garden, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 12 meters.
Explanation
Let ‘s’ 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 + s 60 = 48 + s s = 60 – 48 = 12 s = 12 Therefore, the missing side is 12 meters.
Problem 2
A wire with a perimeter of 360 inches is reshaped into a square. Find the length of each side of the square and divide the total length by 4.
90 inches
Explanation
Given that the perimeter of the wire is equal to the total length of the wire and this wire is reshaped into a square, here is the solution: Perimeter of the wire = Total length of the wire Length of the wire used = Perimeter of the square formed Perimeter of a square = 4 × s 360 = 4 × s 360 ÷ 4 = 90 s = 90 Therefore, the length of each side of the square is 90 inches.
Problem 3
Find the perimeter of a regular hexagon whose sides are 9 cm.
54 cm
Explanation
Perimeter of hexagon = 6 × side length P = 6 × 9 = 54 Therefore, the perimeter of the hexagon is 54 cm.
Problem 4
Jake is designing a hexagonal flower bed in his backyard. He measures the six sides of the bed: Side A = 3 meters Side B = 5 meters Side C = 4 meters Side D = 3 meters Side E = 5 meters Side F = 4 meters How much fencing should Jake buy to go around the edge of the flower bed?
Jake will need 24 meters of fencing to go around the flower bed.
Explanation
The perimeter of the hexagon is the sum of all six sides. Using the formula: P = a + b + c + d + e + f P = 3 + 5 + 4 + 3 + 5 + 4 = 24 meters.
Problem 5
Find the perimeter of a scalene polygon with sides 11, 9, and 6 meters.
Perimeter = 11 + 9 + 6 = 26 meters.
Explanation
Each side of the scalene polygon has a different length. The entire distance around the polygon is calculated as 26 meters by summing the lengths of the three sides.
FAQs on Perimeter of Polygon
1.Evaluate the perimeter of a quadrilateral if its sides are 2 cm, 7 cm, 5 cm, and 8 cm.
2.What is meant by a polygon’s perimeter?
3.What are the types of polygons?
4.Which polygon has no equal sides?
5.Which polygon has equal sides and angles?
Important Glossaries for Perimeter of Polygon
Perimeter: The total length of the sides of a shape. Polygon: A closed figure with three or more straight sides. Regular polygon: A polygon with all sides and angles equal. Scalene polygon: A polygon with all sides of different lengths. Formula of perimeter: The mathematical expression used to calculate the perimeter of a polygon is the sum of its side lengths.
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
