Question

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

Answer 1

The area of a sector whose perimeter is four times its radius r, is r² sq. units.

Explanation:

Perimeter of sector = 2r + arc length = 2r + rθ = 4r.

So rθ = 2r ⇒ θ = 2 radians.

Area = `1/2 r^2θ` 

= `1/2 r^2·2` 

= r²