Question

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

Answer 1

We know that

$\theta =\frac{l}{r}---\left(1\right)$

we are given that, Area of circle is $25\pi sq.cms$

so, $A=\pi r^2$

$r^2=\frac{A}{\pi }=\frac{25}{\pi }\pi sq.cms$

$r=5cms$

now, we are also given that the perimeter of sector of a circle is

$l=20cms$

now, Area od sector is given by,

$a=\frac{1}{2}{r}^2\theta =\frac{1}{2}{r}^2.\frac{l}{r}$ (from $\left(1\right)$)

$a=\frac{lr}{2}=\frac{20\times 5}{2}=50sq.cms$

$\to$ The Area of sector is $50sq.cms$