Question

OPQ is a sector of a circle with centre O and radius is $15$ cms. If m$\angle$POQ$={30}^o$, find the area enclosed by arc PQ and chord PQ.

Answer 1

Area of $\Delta OPQ=\frac{1}{2}{r}^2\sin \left(\theta \right)=\frac{1}{2}\cdot 225\cdot \frac{1}{2}=\frac{225}{4}$
Area of sector = $\pi \frac{\theta }{{360}^o}\cdot r^2=\frac{225}{12}\pi =\frac{75}{4}\pi$
Area between the chord and arc = Area of sector - Area of triangle = $\frac{75}{4}\pi -\frac{225}{4}=\frac{75}{4}(\pi -3)$