Question

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

Answer 1

area of the sector is 77.51 m²

Answer 2

Answer:

The Area of sector = 45.03 cm².

Step-by-step explanation:

Given: Perimeter of a sector of a circle of radius 5.7 m is 27.2 m.

To find : The area of the sector?

Solution :

We construct the figure for clearance,

Refer the attached figure below.

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,

$OAB = \frac{1}{2} lr$

$OAB = \frac{1}{2}(15.8)(5.7)$

$OAB = \frac{90.06}{2}$

$OAB = 45.03 cm^2$

Hence, the Area of sector = 45.03 cm².