Q. 205.0( 3 Votes )

Find the area of

Answer :

Given,


Radius of circle, r = 42 cm


Let the angle of sector be θ with corresponding arc AB


We know that length of an arc


Where, θ is the angle of sector to the corresponding arc and 'r' is radius of circle.


As the length of arc is 44 cm. Putting values we get,





θ = 60°


Also, In ΔOAB


OA = OB [radii of same circle]


OBA = OAB [Angles opposite to equal sides are equal]


Also,


OBA + OAB + AOB = 180° [Angle sum property]


OBA + OBA + θ = 180°


2OBA + 60° = 180°


OBA = 60°


OBA = OAB = AOB = 60°


OAB is an equilateral triangle.


And area of equilateral triangle with side 'a'



Also, area of a sector


Where, θ is angle of sector and 'r' is the radius of circle.


Area of sector OAB



Area of required segment = area of sector OAB - area of ΔOAB


= (924 - 441√3) cm2

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