The perimeter of a certain sector of a circle is 20cm . If the radius of circle is 6 cm , then find the area of the sector . How to solve this ? Is there any formula for this which is out of NCERT maths TB ? Plz help !

As the radius is given as 6 cm, and the perimeter is 20cm

So the arc length will be 20 - 6- 6 = 8cm

Circumference of a circle is given by 2 πr

So the circumference is 2*π*r = 12π

As 12π subtend 360 degree at the centre

So 8cm will subtend (360/12π )* 8 = 240/π

So the angle subtended by given arc will be 240/π

And the area of the circle is πr

^{2}= π(6)

^{2}

It is the area of full circle, it means 360 degree has area of 36π

As 360 degree = 36π

So for 240/π degree the area will be = (36π/360)*(240/π) = 24cm

^{2}

So the area of the sector is 24cm

^{2}

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