Question

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

HOPE THIS WILL HELP YOU...

Answer 2

Let OAB be the given sector

let arc AB=l
perimeter of setor OAB=27.2m

OA+OB+ar AB=27.2cm

5.7+5.7 +l=27.2

l=27.2-(5.7+5.7)
=27.2-11.4
=15.8cm

Area of setor =1/2 lr
=1/2(15.8)x5.7
=90.06/2
=45.03cm²
∴Area of sector=45.03cm²