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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 π = \(\frac{22}7\))

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Best answer

Given, 

Perimeter of semi-circle = 72 m 

Width of path around it = 3.5 m 

Perimeter of semi-circle = πr + 2r 

\(\frac{22}7\) r +2r = 72

= 22r + 14r = 72 × 7 

r = \(\frac{72\times7}{36}\) = 14 cm 

Radius including the width of path(R) = r+3.5 = 14 + 3.5 = 17.5 m

 So, 

area of path = \(\frac{πR^2}2\) - \(\frac{πr^2}2\)

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