Answer:
[tex]\frac{3600\pi}{(\pi +2)^2}[/tex]
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 = [tex]\frac{60}{(\pi +2)}[/tex]
now,
the area of the semi circle = πr² / 2
on substituting the value, we get
area = [tex]\frac{\pi}{2}\times(\frac{60}{(\pi +2)})^2[/tex]
or
area = [tex]\frac{3600\pi}{(\pi +2)^2}[/tex]
Hence,
the area of the semi-circular region = [tex]\frac{3600\pi}{(\pi +2)^2}[/tex]