Question

The area of a sector whose perimeter is four times its radius r units, is

Options

• \[\frac{r^2}{4}\]

• 2r²  sq. units 

•  r² sq.units 

Answer 1

We know that perimeter of the sector= `2r+θ/360xx2pir`

We have given that perimeter of the sector is four times the radius. 

`2r+θ/360x2pir=4r`

Subtracting 2r from both sides of the equation,

`∴ θ/360xx2pir^=4r-2r`

`∴ θ/360xx2pir=2r`

Dividing both sides of the equation 2r we get,

`θ/360=pi=1`

`∴ θpi/360=1`.............(1)

Let us find the area of the sector.

∴ Area of the sector=`θ/360 pir^2`

Substituting  `θpi/360=1` we get,

Area of the sector=`r^2`

Hence, area of the sector is `r^2 `sq.units