Question

The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. Find the area of the sector.

Answer 1

Let OAB be the given sector.

Then, perimeter of sector OAB = 16.4 cm

⇒ OA + OB + arc AB = 16.4 cm

⇒ 5.2 + 5.2 + arc AB = 16.4

⇒ arc AB = 6 cm

∴ Area of sector OAB = `\frac {1}{2}`

= `\frac{1}{2} × 6 × 5.2  cm^2` 

= 15.6 cm²

Answer 2

Perimeter of the sector = `2r + (2πrθ)/(360^circ)`

⇒ `16.4 = 2 xx 5.2 + (2π xx 5.2 xx θ)/(360^circ)`

⇒ `(2π xx 5.2 xx θ)/(360^circ) = 6`

⇒ `θ = (6 xx 360^circ)/(2π xx 5.2)`

Now, area of sector = `θ/(360^circ) xx πr^2`

= `(6 xx 360^circ)/(2π xx 5.2 xx 360^circ) xx π xx (5.2)^2`

= 15.6 sq. units