Q22 of 68 Page 15

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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