Question

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

Answer 1

Radius = OA = OB (From fig) = r

= 5.7 m

Perimeter = 27.2 m

Let angle subtended at centre = 𝜃

Perimeter =`(theta/360^@× 2pir) `+ O𝐴 + O𝐵

=`theta/360^@`× 2(5.7) × 𝜋 + 2(5.7)

=`(2pi(5.7)theta)/360^@`+ 11.4

`=( pi(5.7)theta)/180^@`+ 11.4

= 27.2

=`(pi(5.7)theta)/180^@`= 15.8

Area of sector = `theta/360^@× pir^2`

`=158.8/360×22/7`× 5.7 × 5.7

= 45.048 cm²