Question

60 meters of fencing is used completely to form an enclosed semi-circular region. What is the area of the semi-circular region?'

Answer 1

Answer:

$\frac{3600\pi}{(\pi +2)^2}$

Step-by-step explanation:

Given:

Perimeter of the semi-circle = 60 m

let the radius of the semi-circle to be 'r'

Also,

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

on equating, we get

( π + 2 ) × r = 60 m

or

r = $\frac{60}{(\pi +2)}$

now,

the area of the semi circle = πr² / 2

on substituting the value, we get

area = $\frac{\pi}{2}\times(\frac{60}{(\pi +2)})^2$

or

area = $\frac{3600\pi}{(\pi +2)^2}$

Hence,

the area of the semi-circular region =  $\frac{3600\pi}{(\pi +2)^2}$