Question

In figure, radius of circle is $3.4cm$ and perimeter of sector $PABC$ is $12.8$ cm. Find $area\left(sectorPABC\right)$.

Answer 1

Given radius $=3.4$cm

Perimeter of sector $=12.8$cm

Perimeter$=2r+2\pi r\frac{\theta }{{360}^o}$

$\frac{12.8}{2r}=1+\frac{\pi \theta }{{360}^o}$

$\frac{\pi \theta }{{360}^o}=1+\frac{12.8}{2\times 3.4}$

$\frac{\pi \theta }{{360}^o}=1.88-1$

$[\frac{\pi \theta }{{360}^o}=0.88]$ ……….$\left(1\right)$

Now area of sector $=\pi r^2\frac{\theta }{{360}^o}$

From equation $\left(1\right)$

Area $=r^2\times 0.88$

Area $=(3.4{)}^2\times 0.88c{m}^2$

Area $=10.17c{m}^2$

Hence area of sector$\left(PABC\right)$ is $10.17c{m}^2$.