Question

The perimeter of a sector of the circle of area 25π sq.cm is 20 cm. Find the area of sector.

Answer 1

Area of circle = πr²

But area is given to be 25π sq.cm.

∴ 25π = πr²  

∴ r² = 25

∴ r = 5 cm

Perimeter of sector = 2r + S

But perimeter is given to be 20 cm.

∴ 20 = 2(5) + S

∴ 20 = 10 + S

∴ S = 10 cm

Area of sector = `1/2 xx "r" xx "S"`

= `1/2 xx 5 xx 10`

= 25 sq. cm.