# if the perimeter of a sector of a circle, of area 25 pi sq. cm is 20 cm. Find the area of sector

We have,
Area of circle = $\pi.\ r^2$ = $25\ \pi.$
Therefore, r = $\sqrt{25} = 5$

P of sector = 20 cm
= $2r + r\times \theta$
$\\20 =10 + 5\times \theta\\ 10 = 5 \theta$

Therefore, $\theta = 2$

Now the area of a sector is given as
$=\left ( \frac{\theta}{360^0} \right )\times \pi\times r^2$
$=\left ( \frac{2}{360^0} \right )\times \pi\times 5^2$
$=\left ( \frac{1}{180^0} \right )\times \pi\times 25$

Thus, the area of the sector is 25 sq.cm

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