Q. 205.0( 3 Votes )

Find the area of

Answer :


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]


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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses