Perimeter 

A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek - peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference.

Calculating the perimeter has considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.     

Perimeter is the distance around a two dimensional shape, or the measurement of the distance around something; the length of the boundary. 

Perimeter of a Triangle

The perimeter of a triangle is;

If the triangle is an equilateral triangle;

, where, 'a' is the length of the sides.

Perimeter of a Square

The perimeter of a square is;

, where, 'a' is the length of the sides.

Perimeter of a Rectangle

The perimeter of a rectangle is;

, where, 'l' is the length and 'b' the breath.

Perimeter of a Quadilateral

The perimeter of a quadilateral is;

Perimeter of a Circle

The perimeter of a circle is;

, where, 'r' is the radius of the circle and '' = 3.14.

Example 1: Find the perimeter of a triangle with sides measuring 5 centimeters, 9 centimeters and 11 centimeters. 

Solution:  P = 5 cm + 9 cm + 11 cm = 25 cm  

Example 2: A rectangle has a length of 8 centimeters and a width of 10 centimeters. Find the perimeter.

 

Solution 1: P = 8 cm + 8 cm + 10 cm + 10 cm = 36 cm.

Solution 2: P = 2(8 cm) + 2(10 cm) = 16 cm + 20 cm = 36 cm. 

The second solution is the more commonly used one.

Example 3: Find the perimeter of a square with each side measuring 2 inches.

Solution 1: P = 2 in + 2 in + 2 in + 2 in = 8 in. 

Solution 2: P = 4x 2in = 8 in.

The second solution is the more commonly used one.

Example 4: Find the perimeter of an equilateral triangle with each side measuring 4 centimeters.

Solution 1: P = 4 cm + 4 cm + 4 cm = 12 cm. 

Solution 2: P = 3 x 4cm = 12 cm

The second solution is the more commonly used one.

A square and an equilateral triangle are both examples of regular polygons. Another method for finding the perimeter of a regular polygon is to multiply the number of sides by the length of one side.  

Example 5: Find the perimeter of a regular pentagon with each side measuring 3 inches.

 

Solution: = 5 x 3 in = 15 in. 

Example 6: The perimeter of a regular hexagon is 18 centimeters. How long is one side?

Solution: We have P = 18 cm

Let us now find the length of one side.

A regular hexagon has 6 sides, so we can divide the perimeter by 6 to get the length of one side ( S ).

 S = 18 cm / 6

S = 3 cm 

Summary

The idea of perimeter is widely used in our daily life.

• A farmer who wants to fence his field.
• An engineer who plans to build a compound wall on all sides of a house.
• A person preparing a track to conduct sports.

All these people use the idea of ‘perimeter’.