Question

The perimeter of a sector of a circle of radius $5.2$ cm is $16.4$ cm. The area of the sector is ____________.

• A. $15.1{\text{cm}}^2$
• B. $15.5{\text{cm}}^2$
• C. $15.6{\text{cm}}^2$
• D. $15.9{\text{cm}}^2$

Answer 1

Answer: (C)

$15.6{\text{cm}}^2$

Let $AOB$ be the sector with $O$ as center.

Given: Radius $=r=5.2$ cm

Perimeter of sector $=16.4$ cm

So, $OA+AB+OB=16.4$

$\Rightarrow 5.2+5.2+AB=16.4$

$\Rightarrow AB=6$ cm

Area of sector $=\frac{1}{2}rl$

$=\frac{1}{2}\times 5.2\times 6$

$=15.6$ cm${}^2$