107 LearnersLast updated on August 5th, 2025
Perimeter of Area
The perimeter of a shape is the total length of its boundary. It is used for fencing a property, sewing, and more. In this topic, we will learn about the perimeter of different areas.
What is the Perimeter of an Area?
The perimeter of an area is the total length of its boundary. To find the perimeter of a shape, add the lengths of all its sides. For instance, if you have a rectangular garden that is 20 meters long and 10 meters wide, the perimeter is 2*(20 + 10) = 60 meters.
Formula for Perimeter of Rectangle - P = 2(l + w).
Let’s consider another example of a rectangular swimming pool with length l = 15 meters and width w = 8 meters. So the perimeter of the rectangle will be: P = 2(l + w) = 2(15 + 8) = 2*23 = 46 meters.
How to Calculate the Perimeter of a Rectangle
To find the perimeter of a rectangle, apply the formula P = 2(l + w). For instance, a given rectangular field has a length of 30 meters and a width of 20 meters. Perimeter = 2*(30 + 20) = 2*50 = 100 meters. Example Problem on Perimeter of Rectangle - For finding the perimeter of a rectangle, we use the formula P = 2(l + w). For example, let’s say, l = 25 meters, w = 15 meters. Now, the perimeter = 2*(25 + 15) = 2*40 = 80 meters. Therefore, the perimeter of the rectangle is 80 meters.
Tips and Tricks for Perimeter of Area
Learning some tips and tricks makes it easier for children to calculate the perimeter of different shapes. Here are some tips and tricks given below: Always remember that a rectangle's perimeter is calculated using the formula P = 2(l + w), where l is the length and w is the width. Calculating the perimeter of a shape starts by determining the length of each side. For irregular shapes, measure all sides accurately. To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of shapes. After that, apply the appropriate formula to each shape. 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 Area
Did you know that while working with the perimeter of different areas, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:
Mistake 1
Incorrectly using formulas for different shapes.
Remember that specific shapes have specific formulas for their perimeter. Ensure you use the correct formula for the shape you're dealing with.
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 around a shape, while the area, in square units, represents the space inside the shape.
Mistake 3
Assuming all sides of a shape are equal, leading to inaccurate calculations.
Always check if the shape is regular or irregular. If irregular, measure each side separately for an accurate perimeter calculation.
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 shape.
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 shape to accurately identify the side lengths.
Perimeter of Area Examples
Problem 1
A rectangular garden has a perimeter of 100 meters, with one side measuring 30 meters. To find out the length of the missing side, subtract the sum of the known sides from half the perimeter.
Length of the missing side = 20 meters.
Explanation
Let ‘w’ be the width of the rectangle. And the given perimeter = 100 meters. Length = 30 meters. Perimeter of rectangle = 2(l + w). 100 = 2(30 + w). 50 = 30 + w. w = 50 - 30 = 20. Therefore, the missing side is 20 meters.
Problem 2
A wire with a perimeter of 240 inches is reshaped into a square. Find the length of each side of the square.
60 inches.
Explanation
Given that the perimeter of the wire is equal to the perimeter of the square: Perimeter of a square = 4 × side. 240 = 4 × side. 240 ÷ 4 = 60. Therefore, the length of each side of the square is 60 inches.
Problem 3
Find the perimeter of a regular hexagon whose sides are 8 cm.
48 cm.
Explanation
Perimeter of hexagon = 6 × side. P = 6 × 8 = 48. Therefore, the perimeter of the hexagon is 48 cm.
Problem 4
Liam is planning a circular flower bed in his backyard. If the diameter of the flower bed is 10 meters, how much fencing should Liam buy to go around the edge of the bed?
Liam will need approximately 31.4 meters of fencing.
Explanation
The perimeter (circumference) of a circle is calculated using the formula: C = π × diameter. Using π ≈ 3.14, C = 3.14 × 10 = 31.4 meters.
Problem 5
Find the perimeter of a pentagon with sides measuring 9, 9, 9, 9, and 9 cm.
Perimeter = 9 + 9 + 9 + 9 + 9 = 45 cm.
Explanation
Each side of the pentagon has the same length. The entire distance is calculated around the pentagon by summing the lengths of the five sides, resulting in 45 cm.
FAQs on Perimeter of Area
1.Calculate the perimeter of a rectangle if its length is 12 cm and width is 5 cm.
2.What is meant by an area’s perimeter?
3.What are the types of shapes?
4.Which shape has equal sides and angles?
5.How is the perimeter of a circle calculated?
Important Glossaries for Perimeter of Area
Perimeter: The total length around a shape. Rectangle: A four-sided shape with opposite sides equal. Formula of Perimeter: The mathematical expression used to calculate the perimeter of a shape. Circle: A round shape with all points equidistant from the center. Polygon: A closed figure with three or more 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
