Question

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

(a) $\frac{r^2}{4}$ sq. units

(b) 2r² sq. units

(c) r² sq.units

(d) $\frac{r^2}{2}$sq. units

Answer 1

We know that perimeter of the sector .

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

Subtracting 2r from both sides of the equation,

Dividing both sides of the equation 2r we get,

……….(1)

Let us find the area of the sector.

Substituting we get,

Hence, area of the sector is.

Therefore, the correct answer is (c).