# Find the area of

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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