# The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. Find the area of the sector. - Mathematics

Sum

The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm. Find the area of the sector.

#### Solution

Let OAB be the given sector. Then,

Perimeter of sector OAB = 16.4 cm

⇒ OA + OB + arc AB = 16.4 cm

⇒ 5.2 + 5.2 + arc AB = 16.4

⇒ arc AB = 6 cm

⇒ / = 6 cm

∴ Area of sector OAB = \frac { 1 }{ 2 }

= \frac { 1 }{ 2 } × 6 × 5.2 cm^2 = 15.6 cm^2

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