If the perimeter of a sector of a circle of radius 5.6 cm is 17.2 cm, find the area of the sector

If the perimeter of a sector of a circle of radius 5.6 cm is 17.2 cm,

1.	If the perimeter of a sector of a circle of radius 5.6 cm is 17.2 cm, find the area of the sector
Answer» Let OAB be the given sectorLet arc AB =\xa0{tex}l{/tex}Perimeter of sector OAB = 27.2m{tex} \\Rightarrow {/tex}\xa0OA + OB + ARC AB = 27.2{tex} \\Rightarrow {/tex}\xa0{tex}l{/tex} = 27.2 - (5.7 + 5.7) = 15.8MNow, length of arc\xa0{tex} = \\frac{\\theta }{{360}} \\times 2\\pi r{/tex}{tex}\\frac{{15.8}}{{2\\pi r}} = \\frac{\\theta }{{360}}{/tex}Area of sector AOB\xa0{tex} = \\frac{\\theta }{{360}} \\times \\pi {r^2}{/tex}{tex} = \\frac{{5.8}}{{2\\pi r}} \\times \\pi {r^2}{/tex}= 7.9r{tex} = 7.9 \\times 5.7{/tex}= 45.03m2