In the given figure PQRS is a square of side 2 units. With SR as diameter, a semicircle is drawn. PTR and QTS are quadrants of circles of radius 2 units. If the shaded area is $\frac{\mathrm{n}}{\mathrm{n}+1}\mathrm{\pi }-\sqrt{3}$then n is

In the given figure PQRS is a square of side 2 units. With SR as diameter, a semicircle is drawn. PTR and QTS are quadrants of circles of radius 2 units. If the shaded area is$\frac{\mathrm{n}}{\mathrm{n}+1}\mathrm{\pi }-\sqrt{3},\mathrm{then} \mathrm{n} \mathrm{is}$
sol : $\begin{array}{l}2\left(\frac{1}{2}(2{)}^2\frac{\mathrm{\pi }}{3}-\frac{\sqrt{3}}{2}\right)-\frac{\mathrm{\pi }(1{)}^2}{2}\\ \frac{4\mathrm{\pi }}{3}-\sqrt{3}-\frac{\mathrm{\pi }}{2}=\frac{5\mathrm{\pi }}{6}-\sqrt{3}\\ \mathrm{n}=5\end{array}$