Question

Find the area of the shaded part. (Give your answers in terms of $\mathrm{\pi }$)

Answer 1

Area of the shaded portion = Area of sector I + Area of sector II

= $\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{r}^2$ +$\frac{\mathrm{\theta }}{360}\times \mathrm{\pi }{r}^2$

= $\frac{90}{360}\times \mathrm{\pi }\times 4^2$ + $\frac{30}{360}\times \mathrm{\pi }\times 3^2$

= $\left(4\mathrm{\pi }+\frac{3}{4}\mathrm{\pi }\right){\mathrm{cm}}^2$