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

Options

A. ` 14 . 6 cm^(2)`
B. ` 15 . 6 cm ^(2)`
C. ` 16 . 6 cm ^(2)`
D. `12 . 6 cm ^(2)`

Answer

B

Explanation

Let OAB be the given sector

Then ,
Perimeter of sector OAB = 16 . 4 cm
` rArr OA + OB + arc AB = 16 . 4 cm `
`rArr 5 . 2 + 5 . 2 + arc AB =16 . 4`
` rArr ` arc AB = 6 cm
`:. 1 = 6 cm`
`:. ` Area of sector OAB ` = (1)/(2) lr = (1)/(2) xx 6 xx 5 . 2 cm^(2)`
` = 15 . 6 cm ^(2)`