Question

The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.

Answer 1

Let $OAB$ be a the given sector with perimeter $27.2cm$
Let arc $AB=l$
Perimeter of sector $OAB=27.2cm$
$\Rightarrow OA+AB+OB=27.2$
$\Rightarrow 5.6+l+5.6=27.2$
$\Rightarrow l=27.2-11.2$
$\Rightarrow l=16cm$
Now, we know that
Length of the arc=$\frac{\theta }{360}\times 2\pi r$
$\Rightarrow 16=\frac{\theta }{360}\times 2\pi r$
$\Rightarrow \frac{16}{2\pi r}=\frac{\theta }{360}$....(i)
Area of sector $OAB=\frac{\theta }{360}\times \pi r^2$
=$\frac{16}{2\pi r}\times \pi r^2$[from(i)]
=$8r$
=$8\times 5.6$
=$44.8c{m}^2$