Question

 A path of width 3.5 m  runs around a semi-circular grassy plot whose perimeter is 72 m . Find the area of the path .

`("Use"  pi= 22/7) ` 

Answer 1

Let the radius of the semicircular plot be r. 
Perimeter of the semi-circular grassy plot = `pi r+2r=72` 

`⇒ r=14 cm` 

Given that the width of the plot = 3.5 m
Thus, the outer radius = 3.5 + 14 = 17.5 m

Area of the path = `(pi R^2)/2-(pi r^2)/2`

`= pi/2 (R^2-r^2)` 

`=pi/2 ((17.5)^2-(14)^2)` 

`= 173.25 m^2`