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The perimeter of certain sector of circle of radius 5.6 m is 27.2 m. Find the area of sector.
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ЁЭЬГ = 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`× ЁЭЬГ = 16 × 180
⇒ ЁЭЬГ `=(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
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