Question

The perimeter of a sector of a circle, of area $25\pi sq.cms.$ is $20cms.$ Find the area of sector.

Answer 1

A] Area of circle $=\pi r^2=25\pi$

$\therefore r^2=25$

r = 5 cm

Perimeter of sector = r + r + 5 = 20

$=2r+r\theta =20$

$r(2+\theta )=20$

$\therefore 5(2+\theta )=20$

$2+\theta =4$

$\theta =2^{\circ }$

$\therefore$ area of sector $=\frac{1}{2}{r}^2\theta$=$\frac{1}{2}\times 25\times 2$=$25c{m}^2$