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131 LearnersLast updated on December 11, 2025
Perimeter of Figure
The perimeter of a shape is the total length of its boundary. The perimeter is calculated by summing the lengths of all sides of the figure. It is used for various practical applications such as fencing a property, sewing, and more. In this topic, we will learn about the perimeter of different figures.
What is the Perimeter of a Figure?
The perimeter of a figure is the total length of its sides.
For any polygon, the perimeter is found by adding the lengths of all its sides.
For example, the formula for the perimeter of a rectangle is P = 2 × (l + w), where l and w are the length and width of the rectangle.
Similarly, for a square with side length s, the perimeter is P = 4s..
Formula for Perimeter of a Rectangle - \( P = 2 \times (l + w) \).
Let’s consider an example of a rectangle with length l = 8 and w = 5.
So the perimeter of the rectangle will be: P = 2 × (l + w) = 2 × (8 + 5) = 2 × 13 = 26.
How to Calculate the Perimeter of a Square
To find the perimeter of a square, simply multiply the side length by 4.
For instance, if a square has a side length of s = 6, then the perimeter is P = 4 x 6 = 24.
Example Problem on Perimeter of Square - For finding the perimeter of a square, use the formula, P = 4 .
For example, if s = 5, then the perimeter = 4 x 5 = 20. Therefore, the perimeter of the square is 20 units.
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Tips and Tricks for Calculating Perimeter
Learning some tips and tricks makes it easier for children to calculate the perimeter of various figures. Here are some tips and tricks given below:
Always remember that the perimeter is simply the sum of the sides of the shape.
For a rectangle, use the formula P = 2 x (l + w), and for a square, P = 4s.
Calculating the perimeter of a polygon with more than four sides may involve finding the length of each side using the distance formula.
The distance formula is: Distance = √((xโ − xโ)² + (yโ − yโ)²).
Here, (xโ, yโ) and (xโ, yโ), indicate the positions of two points that form a side of the polygon.
To reduce confusion, specifically arrange the indicated side lengths if you need the perimeter of a group of different polygons.
After that, apply the relevant formula to each shape.
To avoid mistakes when adding the perimeter, ensure 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.
This is often used in area-related calculations, like Heron’s formula for triangles.
Common Mistakes and How to Avoid Them in Perimeter Calculation
Did you know that while working with the perimeter of figures, 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 not applicable to the shape.
Remember that each shape has its specific perimeter formula.
For instance, using the formula for a triangle on a square will lead to errors. Know the shape and apply the correct formula.
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 figure’s sides, while the area, in square units, represents the space inside the figure.
Mistake 3
Assuming all shapes are regular, which results in inaccurate calculations.
Shapes like scalene triangles or irregular polygons have sides of different lengths.
Always be careful about the type of the shape 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 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 a diagram to accurately identify the side lengths.
Perimeter of Figure Examples
Problem 1
A garden in the shape of a rectangle has a perimeter of 100 meters. If the length of the garden is 30 meters, find the width.
The width of the garden is 20 meters.
Explanation
Let w be the width of the garden.
The given perimeter P = 100 meters.
l = 30 meters.
Perimeter of a rectangle = 2 × (l + w)
100 = 2 × (30 + w)
100 = 60 + 2w
2w = 100 − 60 = 40
w = 40 / 2 = 20 meters.
Therefore, the width is 20 meters.
Problem 2
A wire with a perimeter of 200 inches is reshaped into a square. Find the length of each side of the square.
50 inches
Explanation
Given that the wire is reshaped into a square, here is the solution: Perimeter of the square = Total length of the wire
Length of the wire used = Perimeter of the square formed
Perimeter of a square = 4s
200 = 4s
s = 200 ÷ 4 = 50
s = 50.
Therefore, the length of each side of the square is 50 inches.
Problem 3
Find the perimeter of a regular hexagon whose sides are 7 cm.
42 cm
Explanation
Perimeter of a regular hexagon = 6 × side length
P = 6 × 7 = 42.
Therefore, the perimeter of the hexagon is 42 cm.
Problem 4
Annie is planning a rectangular vegetable garden with a length of 12 meters and a width of 8 meters. How much fencing does Annie need to go around the garden?
Annie will need 40 meters of fencing to go around the garden.
Explanation
The perimeter of a rectangle is calculated as P = 2 x (l + w).
Using the formula: P = 2 x (12 + 8) = 2 x 20 = 40 meters.
Problem 5
Find the perimeter of a trapezoid with sides measuring 10 m, 8 m, 5 m, and 7 m.
The perimeter is 30 meters.
Explanation
The perimeter of a trapezoid is the sum of all its sides.
P = 10 + 8 + 5 + 7 = 30 meters.
FAQs on Perimeter of Figure
1.Evaluate the perimeter of a rectangle if its length is 10 cm and width is 5 cm.
2.What is meant by a figureโs perimeter?
3.What are the common 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 Figure
- Perimeter: The total length of the sides of a shape.
- Rectangle: A polygon with four sides and opposite sides of equal length.
- Square: A polygon with four equal sides and four right angles.
- Hexagon: A polygon with six sides.
- Trapezoid: A four-sided figure with one pair of parallel sides.
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
