Question

The perimeter of certain sector of circle of radius 5.6 m is 27.2 m. Find the area of sector.

Answer 1

𝜃 = angle subtended at centre

Radius (r) = 5.6m = OA ± OB

Perimeter of sector = 27.2 m

(AB arc length) + OA + OB = 27.2

⇒`(theta/360^@× 2pir)` + 5.6 + 5.6 ± 27.2

⇒`(5.6 pitheta)/180^@`+ 11.2 = 27.2

⇒ `5.6 ×22/7`× 𝜃 = 16 × 180

⇒ 𝜃 `=(16×180)/(0.8×22)`= 163.64°

Area of sector =`theta/360^@× pir^2 =163.64^@/360^@×22/7`× 5.6 × 5.6

=`163.64/180`× 11 × 0.8 × 5.6

= 44.8 cm²