Perimeter is defined as the total length of all the sides of a closed figure. It is measured in units of length, such as meters, centimeters, or inches.
- The perimeter of a shape can be found by adding the lengths of all the sides.
For example, a square with a side length of 5 m is 5 + 5 + 5 + 5, i.e., 20 m. - The perimeter of a shape is the distance you cover when you walk around it.
Formulas for Perimeter
Different shapes have specific formulas to calculate their perimeter.
- Polygon: Sum of all sides
- Regular Polygon: Perimeter = n × side length
Common Shapes
Name of Shape | Perimeter Shape |
|---|---|
a + b + c | |
4a | |
2(L + B) | |
Sum of All Four Sides: a + b + c + d | |
2(a + b) | |
Sum of All Sides | |
2nR sin (180°/n) |
How to Find Perimeter
To calculate the perimeter of any figure, we use the steps discussed below:
Step 1: Find the length of all the sides of the given figure and mark them as a, b, and c
Step 2: Find the sum of all the sides to get the perimeter of the figure.
Step 3: If the given figure is a curved figure we use other methods or formulas to find the perimeter of the figure.
Step 4: As the perimeter is nothing but the length of all the sides it is measured in units of length.
For example, suppose we have to find the perimeter of a square plot of side 10 m.
Side of Square (a) = 10 m
Perimeter of Square(P) = 4(a)
P = 4(10) = 40 m
Thus, the perimeter of the square feild is 40 m
Perimeter of Complex Shapes
The perimeter of complex shapes can be calculated by dividing them into simpler parts. Then, add the outer boundary lengths only.
For example, the perimeter of the following shape can be found by breaking it down into a rectangle and a triangle, as it is made of an isosceles triangle and a rectangle.
Solution:
- Sides of the Isosceles Triangle = 8 m
- Length of the Rectangle = 10 m
- Breadth of the Rectangle = 6 m
Observing the figure, the perimeter of the figure is,
Perimeter(P) = 8 + 8 + 10 + 10 + 6
P = 42 m
