Find the area of a shaded region in the Fig.15.73, where a circular arc of radius 7cm has been drawn with vertex A of an equilateral triangle ABC of side 14cm as centre.
Given,
Radius = 7cm
Side of equilateral triangle = 14cm
Area of circle =
Area of circle = 
Area of equilateral triangle = 
Area of equilateral triangle = 
= 
We know that an equilateral triangle always subtend an angle of 60 at centre area of sector = 
=
=
= 25.666cm2
This area is common in both the figure so,
Area of shaded region = (area of circle + area of equilateral triangle - 2×area of sector)
= (154+84.77-2×25.67)
= (238.77-51.33) = 187.44cm2
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