Question

The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

Answer 1

Given:
Radius of a circle(OA,OB) = 5.7 cm
Perimeter of the sector of a circle= 27.2 cm
Let OAB be the given sector.
Perimeter of the sector OAB = 27.2 cm
OA + OB +Arc AB = 27.2 cm
5.7 +5.7 + Arc AB = 27.2
11.4 + Arc AB = 27.2 cm
Arc AB = 27.2 - 11.4 = 15.8 cm Now arc AB is also the length of the sector AB
$\to$ Length of the sector AB(l)= 15.8 cm
$\to$ Area of sector OAB = $\frac{1}{2}$. (length of the arc) (radius )

$\to$ $\frac{1}{2}$ . (15.8) (5.7)
$\to$ = $\frac{90.6}{2}$
$\to$ = 45.03${cm}^2$
Hence, the Area of sector= 45.03${cm}^2$