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 !
A sector is made up of two radius and one arc.
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 πr2 = 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) = 24cm2
So the area of the sector is 24cm2
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 πr2 = 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) = 24cm2
So the area of the sector is 24cm2