Question

The perimeter of a certain sector of a circle of radius 6.5 cm in 31 cm. Find the area of the sector.

The perimeter of a sector of a circle with radius 6.5 cm is 31 cm, then find the area of the sector.

Answer 1

Given:

Radius = 6.5 cm

Let O be the centre of the circle with radius 6.5 cm and OACBO be its sector with perimeter 31 cm.

Thus, we have:

OA + OB + arc AB = 31 cm

⇒ 6.5 + 6.5 + arc AB = 31 cm

⇒ arc AB = 18 cm

Now, Area of the sector OACBO

= `1/2 xx "Radius" xx "arc"`    

= `1/2 xx 6.5 xx 18`

= 58.5 cm² 

Answer 2

Given, Radius = 6.5 cm

Let O be the centre of a circle with radius 6.5 cm and OACBO be its sector with perimeter 31 cm.

Thus, we have

OA + OB + arc ACB = 31 cm

⇒ 6.5 + 6.5 + arc ACB = 31 cm

⇒ arc ACB = 18 cm

Now, Area of sector OACBO

= `1/2 xx "radius" xx "arc ACB"`

= `1/2 xx 6.5 xx 18`

= 58.5 cm²