The perimeter of a sector of acircle of radius 5.7 is27.2.find the are

1.	The perimeter of a sector of acircle of radius 5.7 is27.2.find the area of sector
Answer» Let O be the centre of the circlewhose radius is 5.7 cm.Let OAB be the sector withperimeter 27.2 cm, Then,{tex}\\mathrm { OA } + \\mathrm { OB } + \\operatorname { arcACB } = 27.2{/tex}{tex}\\Rightarrow 5.7 + 5.7 + \\operatorname { arc } A C B = 27.2{/tex}{tex}\\Rightarrow 11.4 + \\operatorname { arc } A C B = 27.2{/tex}{tex}\\Rightarrow \\operatorname { arc } A C B = 27.2 - 11.4 = 15.8 \\mathrm { cm }{/tex}{tex}\\Rightarrow \\frac { \\theta } { 360 } \\times 2 \\pi r = 15.8{/tex}{tex}\\Rightarrow \\frac { \\theta } { 360 } \\times 2 \\times \\frac { 22 } { 7 } \\times 5.7 = 15.8{/tex}{tex}\\Rightarrow \\theta = \\frac { 15.8 \\times 360 \\times 7 } { 2 \\times 22 \\times 5.7 }{/tex}{tex}\\therefore {/tex}\xa0Area of the sector =\xa0{tex}\\frac { \\theta } { 360 } \\times \\pi r ^ { 2 }{/tex}{tex}= \\frac { 15.8 \\times 360 \\times 7 } { 2 \\times 22 \\times 5.7 \\times 360 } \\times \\frac { 22 } { 7 } \\times ( 5.7 ) ^ { 2 }{/tex}= 45.03 cm2

The perimeter of a sector of acircle of radius 5.7 is27.2.find the area of sector