Perimeter

Perimeter is defined as the sum of all the sides of any polygon. The perimeter of any figure is the sum of the length of all the boundaries of that figure. Perimeter of any figure gives us the length of all the boundaries we can understand this by the following example, suppose we have to find the length of wire required to fence a square then the perimeter of the square field gives the required result as it gives the length of the boundary of the square field.

In this article we will learn about Perimeter, how to calculate the perimeter, various formulas used to calculate the perimeter, examples of the perimeters, and others in detail.

What is Perimeter?

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, centimetres, or inches. The perimeter of a shape can be found by adding the lengths of all the sides. For example, the perimeter of a square with a side length of 5 m is 20 m

Perimeter of any figure is widely used in geometry for other calculations as it is used to find the Area and other things related to the figure. Suppose we are given the perimeter of any regular figure then using the perimeter formula we can easily find the length of the side of the figure, which is used further to find the area and other perimeters of the figure.

Perimeter Formula

The perimeter of various shapes can easily be found using the formula,

Perimeter of Polygon = Sum of All Sides

So, if the sides of any polygon are given then its perimeter can be easily found using the formula discussed above.

Suppose we are given a regular polygon of side n, then its perimeter is calculated using the formula,

Perimeter of Regular Polygon = n × sides

The perimeter formula for some specific figures is,

• A square is a regular polygon with four sides and the formula for the perimeter of the square is,

Perimeter of Square = 4a units

where a is the length of the square

• A rectangle is a polygon with four sides in which the opposite sides are parallel and equal and the formula for the perimeter of the rectangle is,

Perimeter of Rectangle = 2(l+b) units

where, 

• l is the length of the rectangle
• b is the base of the rectangle

• A triangle is a polygon with three sides it is the simplest polygon possible and the formula for the perimeter of the triangle is,

Perimeter of Triangle = (a+b+c) units

where a, b, and c are the length of the side of the triangle

• A circle is a curved figure in which the distance of the curve is always fixed from the center of the curve. The perimeter of the circle is also called the circumference of the circle, and the formula to find the circumference of the circle is,

Circumference of Circle = 2πr units

where, r is the radius of the circle.

Perimeter Units

The perimeter of any figure is nothing but the sum of the length of all the sides of any polygon. So the perimeter is measured in units of length, i.e. m, cm, etc. If the given figure or structure is very large its perimeter can also be measured in Kilometers or any other unit of length.

How to Find Perimeter?

To find 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 Simple Shapes

The perimeter of simple shapes can be found using formulas. Some common simple shapes include squares, rectangles, triangles, circles, and trapezoids.

Name of Shape	Perimeter Formula
Circle	2πr
Triangle	a+b+c
Square	4a
Rectangle	2(L+B)
Quadrilateral	Sum of All Four Sides: a+b+c+d
Parallelogram	2(a+b)
Any Polygon	Sum of All Sides
Regular Polygon	2nR sin (180°/n)

Perimeter of Complex Shapes

Perimeter of complex shapes can easily be found by breaking the complex shape into smaller shapes whose perimeter can be easily found. Then the perimeters of the smaller shapes can then be added together to find the perimeter of the complex shape.

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

Difference Between Perimeter and Area

The differences between Perimeter and Area are discussed in the table added below,

Perimeter	Area
Perimeter is the sum of the length of the boundaries of any figure.	Area is the space occupied by the boundaries of the figure.
Perimeter of any figure is measured in units of length.	Area of any figure is measured in unit2, i.e. m2, cm2, etc.
Basic formula used for finding the perimeter is, Perimeter = Sum of All Side	Basic formula used for finding the area is, Area = Base × Height
Some Basic Perimeter Formulas are, Perimeter of Square = 4a Perimeter of Rectangle = 2(l+b) Circumference of Circle = 2πr	Some Basic Area Formulas are, Area of Square = a2 Area of Rectangle = l ×  b Area of Circle = πr2
It is used for finding the fence and other things in the figure.	It is used for finding the floor area and other things related to the figure.

Read More,

• Area of Rectangle
• Area of Circle
• Area of Triangle

Solved Examples on Perimeter

Example 1: Find the Perimeter of a Square with a side length of 5 meters.

Solution:

Given,

• Side of Square(a) = 5 m

Perimeter of Square(P) = 4a

P = 4(5)

P = 20 m

Thus, the perimeter of the square is 20 m.

Example 2: Find the Perimeter of a Rectangle with a length of 10 meters and a width of 5 meters.

Solution:

Given,

• Length of Rectangle(l) = 10 m
• Breadth of Rectangle(b) = 5 m

Perimeter of Rectangle(P) = 2(l+b)

P = 2(10+5)

P = 30 m

Thus, the perimeter of the rectangle is 30 m.

Example 3: Find the Perimeter of a Triangle with side lengths 3 meters, 4 meters, and 5 meters.

Solution:

Given,

• First Side (a) = 3 m
• Second Side (b) = 4 m
• Third Side (c) = 5 m

Perimeter of Triangle (P) = a + b + c

P = 3 + 4 + 5

P = 12 m

Thus, the perimeter of the triangle is 12 m

Example 4: Find the Perimeter(Circumference) of a circle with a radius of 7 meters.

Solution:

Given,

• Radius of Circle(r) = 7 m

Circumference of Circle(C) = 2πr

C = 2×22/7×7

C = 44 m

Thus, the circumference of the circle is 44 m.

Example 5: Find the perimeter of a Trapezium with bases 6 meters and 8 meters, and height 4 meters.

Solution:

Given,

• Base of Trapezoid, b₁ = 6 m and b₂ = 8 m
• Height of Trapezoid(h) = 4 m

Perimeter of Trapezium(P) = (b₁ + b₁) + 2h

P = (6+8) + 2(4)

P = 22 m

The Perimeter of the Trapezum is 22 m.

FAQs on Perimeter

What is Perimeter of any Polygon?

Perimeter of any shape is defined as the sum of all the sides and is the total length of the boundary of the given figure. Thus, the perimeter of the n-sided polygon is the sum of the length of all the sides of the polygon.

How is Perimeter different from Area?

Perimeter and the area are two different parameters used for measuring various aspects of any figure. The perimeter as we know is used to measure the length of the boundaries of the figure. Whereas the area is the measure of the space occupied inside the boundary of the figure.

How is Perimeter Calculated?

Perimeter of any figure is calculated using the formula,

Perimeter of Any Figure = Sum of the Length of All the Sides

What are Some Common Formulas used for Calculating  Perimeters?

Some formulas used for calculating the perimeters of various shapes are,

• Perimeter of Rectangle = 2(Length + Width)
• Perimeter of Square = 4 × Side Length
• Perimeter of Triangle = Sum of All Three Side Lengths
• Circumference of Circle = 2 × π × Radius

How is Perimeter Used in Real-Life Situations?

Perimeter has practical applications in various areas. For example, in construction, it helps determine the amount of material needed for fencing or outlining a building. In landscaping, it helps calculate the length of borders or paths.

Can Perimeter be Negative?

As perimeter is the sum of all the sides of a polygon, and the length of a side can never be negative the perimeter of any figure can never be negative.