Question

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

Answer 1

Let OAB be the given sector. Then,

Perimeter of sector OAB = 16.4 cm

⇒ OA + OB + arc AB = 16.4 cm

⇒ 5.2 + 5.2 + arc AB = 16.4

⇒ arc AB = 6 cm

⇒ / = 6 cm

∴ Area of sector OAB = ${\displaystyle \frac{1}{2}}$

${\displaystyle =\frac{1}{2}\times 6\times 5.2c{m}^2=15.6c{m}^2}$