Question

The perimeter of a sector of a circle of area $25\pi \text{sq. cm}$ is $20\text{cm}$. Find the area of the sector?

Answer 1

Since area of circle is equal to $25\pi \text{sq. cm}$.

$\Rightarrow \pi r^2=25\pi \Rightarrow r=5\text{cm}$

Let us assume that the length of the arc of the sector is equal to $s$.

Perimeter of sector is also given and that is equal to $20$.

$\Rightarrow 2r+s=20\Rightarrow 10+s=20\Rightarrow s=10$

Now,

$\begin{array}{cc}\theta & =\frac{s}{r}\\ & =\frac{10}{5}\\ & =2\end{array}$

$\begin{array}{cc}\text{Area of sector}& =\frac{\theta }{2\pi }\cdot \pi r^2\\ & =\frac{2}{2\pi }\cdot \pi 5^2\\ & =25{\text{cm}}^2\end{array}$