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

The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm find

1.	The perimeter of a sector of a circle of radius 5.2 cm is 16.4 cm find the area of the sector
Answer» Let OAB be the given sector.It is given that Perimeter of sector OAB = 16.4 cm{tex}\\Rightarrow{/tex}OA + OB + arc AB = 16.4 cm{tex}\\Rightarrow{/tex}5.2 + 5.2 + arc AB = 16.4{tex}\\Rightarrow{/tex}arc AB = 6 cm\xa0{tex}\\Rightarrow{/tex}l = 6 cm{tex}\\therefore{/tex}Area of sector OAB ={tex}\\frac { 1 } { 2 } l r = \\frac { 1 } { 2 } \\times 6 \\times 5.2 \\mathrm { cm } ^ { 2 }{/tex}= 15.6 cm2