Question

if the perimeter of a sector of circle of radius 5.7cm is 27.2cm then find area of corresponding 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
Length of the sector AB(l)= 15.8 cm
Area of sector OAB = ½ le
= ½(15.8)(5.7) = 90.06 /2= 45.03 cm²
Hence, the Area of sector= 45.03 cm².