PERIMETER OF A SEMICIRCLE – MINDSPARK

PERIMETER OF A SEMI-CIRCLE

Perimeter is nothing but the length of the boundary. A semicircle is the half of a circle so the perimeter of a semicircle is the length of the boundary as shown in the figure below:

The black border is the boundary or the perimeter of the semicircle. O is the centre and the length from A to B through the centre is the diameter. The length from O to A is equal to the length from O to B and is the radius of the semicircle. Radius is equal to half the length of the diameter of the semicircle.

HOW TO FIND THE PERIMETER OF THE SEMICIRCLE?

It is easy to find the perimeter of the semicircle. We need to know the formula for the perimeter of a circle. 

Perimeter of the circle = 2πr

We will divide the perimeter by 2 to find the curved part of the semicircle which will give us

\frac{2 \pi r}{2}=\pi r

When we find the perimeter of the semicircle, the boundary does not include the line AB which is the diameter. Here, in the case of the semicircle, we will need to include the diameter (denoted as d) as well since it counts as the boundary or the perimeter of the semicircle

Perimeter of the semi-circle =  (πr + d)

Now, we know that d = 2r or diameter is twice the radius. Replacing the value of d we get,

Perimeter of the semi-circle =  (πr + 2r)

Perimeter of the semi-circle =  r(π + 2)

Where the value of π is \frac{22}{7} \text { or } 3.14 which is a constant.

EXAMPLES:

1. What will be the perimeter of a semicircle which has a radius of 7 cm?

Ans:

Perimeter of the semi-circle

=7\left[\frac{22}{7}+2\right]

=7\left[\frac{22+14}{7}\right]

= 36 cm

Therefore, the perimeter is 36 cm.

2. Find the radius of the semicircle whose perimeter is 72 cm.

Ans: 72=r\left[\frac{22}{7}+2\right]

\Rightarrow 72=r\left[\frac{22+14}{7}\right]

\Rightarrow 72=r\left[\frac{36}{7}\right]

\Rightarrow\frac{(72)(7)}{36}=r

∴ r = 14

Therefore, the radius is 14 cm.