107 LearnersLast updated on August 5th, 2025
Perimeter of Irregular Polygon
The perimeter of a shape is the total length of its boundary. The sum of all the sides is called the perimeter of an irregular polygon. Perimeter is also used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of an irregular polygon.
What is the Perimeter of an Irregular Polygon?
The perimeter of an irregular polygon is the total length of all its sides. By adding the length of all the sides, we get the perimeter of the shape. There is no specific formula for the perimeter of an irregular polygon; instead, we use the sum of each side's length. For instance, if a polygon has sides measuring 5, 8, 12, and 9, then its perimeter is P = 5 + 8 + 12 + 9 = 34.
Example Calculation for Perimeter of an Irregular Polygon
Let’s consider an example of an irregular polygon with side lengths: 7, 5, 11, and 6. So the perimeter of the polygon will be: P = 7 + 5 + 11 + 6 = 29.
How to Calculate the Perimeter of an Irregular Polygon
To find the perimeter of an irregular polygon, sum all the side lengths of the polygon. For instance, consider a polygon with the sides of 4, 9, 13, and 7. Perimeter = sum of all sides = 4 + 9 + 13 + 7 = 33 cm. Example Problem on Perimeter of an Irregular Polygon - For finding the perimeter of an irregular polygon, sum up all the side lengths. For example, let’s say the sides are 3 cm, 5 cm, 7 cm, and 10 cm. Now, the perimeter = sum of all sides = 3 + 5 + 7 + 10 = 25 cm. Therefore, the perimeter of the polygon is 25 cm.
Tips and Tricks for Perimeter of an Irregular Polygon
Learning some tips and tricks makes it easier to calculate the perimeter of irregular polygons. Here are some tips and tricks given below: Always remember that a polygon's perimeter is simply the sum of all its sides. Calculating the perimeter of an irregular polygon starts by determining the length of each side. If the vertices are given, the distance formula can be useful: Distance = √((x2-x1)² + (y2-y1)²). Here, (x1, y1) and (x2, y2) indicate the positions of two points that make up the polygon’s side. To reduce confusion, arrange the indicated side lengths if you're calculating the perimeter of multiple polygons. After that, apply the sum to each polygon. To avoid mistakes when adding the perimeter, ensure the side lengths are precise and consistent for practical uses like gardening and architecture. If given a semi-perimeter, which is half the perimeter, you can multiply it by 2 to determine the full perimeter. However, semi-perimeter is not commonly used for irregular polygons unless needed for a specific calculation.
Common Mistakes and How to Avoid Them in Perimeter of an Irregular Polygon
When calculating the perimeter of an irregular polygon, people often encounter errors or difficulties. Here are some solutions to resolve these problems:
Mistake 1
Incorrectly assuming formulas for regular polygons apply to irregular polygons.
Remember that irregular polygons do not have a specific formula like regular polygons. Simply sum the lengths of all the sides.
Mistake 2
Confusing 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 all sides are of equal length, resulting in inaccurate calculations.
In irregular polygons, all sides can differ in length. Always carefully measure or identify each side 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 given in a problem outline.
Before starting the calculations, make sure that you understand the problem and, if possible, try to sketch the polygon to accurately identify the side lengths.
Perimeter of Irregular Polygon Examples
Problem 1
A garden path is in the shape of an irregular quadrilateral with a perimeter of 35 meters. Three of its sides measure 10 meters, 8 meters, and 9 meters. To find out the missing side, subtract the sum of the known sides from the total perimeter.
Length of the missing side = 8 meters.
Explanation
Let ‘x’ be the length of the missing side. And the given perimeter = 35 meters. Length of the three sides = 10, 8, and 9 meters. Perimeter of the polygon = sum of lengths of four sides. 35 = 10 + 8 + 9 + x 35 = 27 + x x = 35 – 27 = 8 Therefore, the missing side is 8 meters.
Problem 2
A piece of wire shaped as a pentagon has a perimeter of 55 inches. If four sides measure 12 inches, 7 inches, 15 inches, and 8 inches, find the length of the fifth side.
13 inches
Explanation
Let the fifth side be ‘y’. Given that the total perimeter of the pentagon is 55 inches: Perimeter of the pentagon = 12 + 7 + 15 + 8 + y 55 = 42 + y y = 55 - 42 = 13 Therefore, the length of the fifth side of the pentagon is 13 inches.
Problem 3
Calculate the perimeter of an irregular hexagon with sides measuring 3, 4, 6, 5, 7, and 9 cm.
34 cm
Explanation
Perimeter of hexagon = sum of all sides P = 3 + 4 + 6 + 5 + 7 + 9 = 34 Therefore, the perimeter of the hexagon is 34 cm.
Problem 4
A farmer has a field in the shape of an irregular pentagon. The sides of the field measure 20 meters, 15 meters, 30 meters, 25 meters, and 18 meters. How much fencing is needed to go around the field?
The farmer will need 108 meters of fencing to go around the field.
Explanation
The perimeter of a polygon is the sum of all its sides. Using the formula: P = 20 + 15 + 30 + 25 + 18 = 108 meters.
Problem 5
Find the perimeter of an irregular polygon (quadrilateral) with sides measuring 8, 12, 14, and 9 meters.
The perimeter is 43 meters.
Explanation
Each side of the quadrilateral has a different length. The total perimeter is calculated by summing the lengths of the four sides: 8 + 12 + 14 + 9 = 43 meters.
FAQs on Perimeter of Irregular Polygon
1.Evaluate the polygon’s perimeter if its sides are 5 cm, 10 cm, 8 cm, and 7 cm.
2.What is meant by a polygon’s perimeter?
3.What are the types of polygons?
4.Can a polygon have sides of different lengths?
5.Which polygon has the smallest perimeter for a given area?
Important Glossaries for Perimeter of Irregular Polygon
Perimeter: The total length of the sides of a shape. Polygon: A closed figure with multiple straight sides. Irregular Polygon: A polygon with sides of varying lengths and angles. Distance Formula: A formula used to calculate the length between two points in coordinate geometry. Side Length: The measure of an individual side of 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.
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: She has songs for each table which helps her to remember the tables
