Q12 of 37 Page 13

The perimeter of a sector of a circle of radius 5.6 cm is 27.2 cm. Find the area of the sector.


Let OAB be a the given sector with perimeter 27.2cm


Let arc AB = l


Perimeter of sector OAB = 27.2cm


⇒ OA + AB + OB = 27.2


⇒ 5.6 + l + 5.6 = 27.2


⇒ l = 27.2 – 11.2


⇒ l = 16cm


Now, we know that




…(i)


Area of sector OAB


[from (i)]


= 8r


= 8 × 5.6


= 44.8cm2


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