Question

The perimeter of a sector of a circle of radius 5.2cm is 16 cm. The area of the sector is.............​

Answer 1

Let POQ be the given sector

Given, radius (r) of circle = 5.2 cm

Given perimeter of sector POQ = 16.4 cm

So, OP + OQ + Arc PQ = 16.4 cm

5.2 + 5.2 + Arc PQ = 16.4 cm

Arc PQ = 6 cm

That is, l = Arc length PQ = 6 cm

Therefore,

Area of sector POQ = 1/2 × r × l

= 5.2 x 6 / 2 = 15.6 cm2