A path of width 3.5m runs …

Let x be the radius of the semi-circular path.
Given, perimeter of circular path = 72
{tex} \Rightarrow 2r + \pi r = 72{/tex}
{tex} \Rightarrow r\left( {2 + \pi } \right) = 72{/tex}
{tex} \Rightarrow r\left( {2 + \frac{{22}}{7}} \right) = 72{/tex}
{tex} \Rightarrow r \times \frac{{36}}{7} = 72{/tex}
{tex}\therefore {/tex} Radius of semi-circular grassy plot = 14m

Since a path of width 3.5 m runs around a semi-circular grassy plot whose Perimeter is 72 m
Then, radius of outer semi-circle = 14m + 3.5m = 17.5m
Area of the path = Area of outer semi-circle-Area of inner semi-circle
{tex} = \frac{1}{2}\pi {\left( {17.5} \right)^2} - \frac{1}{2}\pi {\left( {14} \right)^2}{/tex}
{tex} = \frac{1}{2} \times \frac{{22}}{7}\left[ {{{\left( {17.5} \right)}^2} - {{\left( {14} \right)}^2}} \right]{/tex}
{tex} = \frac{{11}}{7}\left[ {31.5 \times 3.5} \right]{/tex}
= 173.25m²