Question

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

Answer 1

Given :

• Radius of sector → 5.7 cm
• Perimeter of sector → 27.2 cm

Have to Find :

• Area of Sector

Solution :-

As we know, the perimeter is :

OA + OB + AB = 27.2 cm

5.7 cm + 5.7 cm + AB = 27.2 cm

→ 27.2 cm - 11.4 cm

→ 15.8 cm

Hence, Length of Arc ( AB) = 15.8 cm

Now, For Area of sector :

$:\implies\sf{OAB = \dfrac{1}{2} \times l \times r}$

$:\implies\sf{OAB = \dfrac{1}{2} \times 15.8 \times 5.7}$

$:\implies\sf{OAB = 45.03cm^{2}}$

Thus, the area of the given sector is :

$\boxed{\therefore{\bf{A = 45.03^{2}}}}$