Perimeter of Polygons

Have you ever walked around the corner (or edge) of a park. After completion of a whole round the distance traveled by you will be exactly equal to the perimeter of a figure.

Therefore, the total distance around the outside of a polygon is known as Perimeter of a polygon. A polygon is a 2-dimensional figure, but the perimeter is a one-dimensional measurement.

It is the measurement of the path that surrounds a two-dimensional shape.

Finding the perimeter of a Polygon:

From the definition of a perimeter, the perimeter is defined the sum of length of each side. Consider for an example, a quadrilateral whose sides are 12, 6, 8 and 9, the perimeter is given by:

Perimeter = 12 + 6 + 7 + 9 = 34

For a Regular polygon, which has all the sides of equal length, the perimeter is defined as,

Perimeter = n.s ,

where, n = number of sides of a polygon,
and s = length of a side

Perimeter of a Triangle:

Imagine that you are asked to find the perimeter of the triangle given in the following figure.Perimeter of a Triangle

If perimeter is the length of the complete boundary of some surface, then individual side lengths should add up to give us the perimeter. Therefore the perimeter of the triangle given above can be calculated as follows.

4 cm + 4 cm + 6 cm

= 14cm

Therefore, the perimeter of the above triangle is 14 cm.

Perimeter of a Square

What if you had to find the perimeter of a square in the image below?Perimeter of a Square

The only information we have regarding the figure above is that it is a square and it has a single side length of 5 cm. But in a square, all four sides are of equal length. Therefore, the perimeter of this square can be calculated as follows.

Method 1: Perimeter: 5 cm + 5 cm + 5 cm + 5 cm

= 4 x 5 cm

= 20 cm

Method 2: As we know, a square is a regular type of a polygon, therefore

Perimeter = n.s

= 4 \(\times \)   5

= 20 cm

Since all squares have the property where all sides are equal, we can generalize a formula for the perimeter of a square.

Perimeter of a square = 4a

where,

a is the length of a side in the square

Perimeter of a Rectangle

A rectangle depicted in the image below has been given to you.Perimeter of a Rectangle

You are asked to find the perimeter of the rectangle and two of the side lengths are given to you. We already know that in a rectangle, opposite side are equal to each other in length. So the perimeter of this rectangle can be calculated as follows.

5 cm + 5 cm + 3 cm + 3 cm

= (2 x 5 cm) + (2 x 3 cm)

= 2 x (5 + 3)

= 16 cm

The formula for calculating the perimeter of a rectangle can therefore be generalised as follows.

Perimeter of a rectangle = 2 x (l + b)

where,

l is the length of the rectangle

b is the breadth of the rectangle

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Practise This Question

Puja is the owner of a farm as shown in the figure. She goes to the market to buy the fence wire for the field. Calculate the minimum length of the wire to be bought by Puja so that the entire farm is covered. (All dimensions are in m)