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MCQ

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

#### Options

\[\frac{r^2}{4}\]

2r

^{2}sq. unitsr

^{2}sq.units

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#### Solution

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 2*r* from both sides of the equation,

`∴ θ/360xx2pir^=4r-2r`

`∴ θ/360xx2pir=2r`

Dividing both sides of the equation 2*r* 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

Concept: Area of Circle

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