Question

In figure $PQRS$ is a square lawn with side $PQ=42$ meters. Tow circular flower beds are there on the sides $PS$ and $QR$ with centre at $O$, the intersections of its diagonals. Find the total area of the two flower beds (shaded parts).

Answer 1

Area of two flower bed= area of semicircle - area of semi- square

$=\frac{\pi r^2}{2}-\frac{a^2}{2}$

$\begin{array}{c}PQ=SP=42cm\\ \therefore 58=\sqrt{2}\times PQ=\sqrt{2}\times 42=59.4m\\ \therefore radius\left(r\right)=\frac{58}{2}=29.7\end{array}$

Area of shaded region

$\begin{array}{c}\frac{\pi {\left(29.7\right)}^2}{2}-\frac{{\left(42\right)}^2}{2}\\ =1385.58-882=503.58m^2\end{array}$