Question

The perimeter of a certain sector of a circle of radius 5.6 m is 20.0 m. Find the area of the sector. 

Answer 1

Let the radius of circle be r and the arc length is `l`

Perimeter of a sector is given as      ...[∵ `l` = rθ]

∴ p = 2r + rθ   

r = 5.6 m

P = 20 m

⇒ 20 = (2 × 5.6) + 5.6 θ

20 − 11.2 = 5.6 θ

⇒ `8.8/5.6 = θ`

θ = `11/7` radian       ...`[∵ 1" radian" = 180/pi "degree"  pi = 22/7]`

`θ = 11/7 xx 180/pi "degree"`

θ = 90° degree

Area of sector = `θ/360 xx pir^2`

= `90/360^"°" xx 22/7 xx 5.6 xx 5.6`

= `1/4 xx 22/7 xx 5.6 xx 5.6`

= `689.92/28`

Area = 24.64 m²