Question

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

Answer 1

$\huge\underline\mathrm\green{Solution:-}$

$\mathrm\red{Given:-}$

Radius of a circle(OA,OB) = 5.6 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

5.6 +5.6 + Arc AB = 27.2

11.2 + Arc AB = 27.2 cm

Arc AB = 27.2 - 11.2 = 16 cm Now arc AB is also the length of the sector AB

$\red\rightarrow{ }$Length of the sector AB(l)= 16 cm

$\red\rightarrow{ }$Area of sector OAB = $\frac{1}{2}$.(length of the arc) (radius)

$\red\rightarrow{ }$$\frac{1}{2}$ . (16) (5.6)

$\red\rightarrow{ }$$\frac{89.6}{2}$= 44.8 $cm^{2}$

$\underline\mathrm\green{Therefore}$ , area of the circle is 44.8$cm^{2}$