Find the area of the shaded region in Fig. 12.22, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.


We know that each interior angle of an equilateral triangle is of measure 60°

Area of sector OCDE = r2


= * * 6 * 6


= cm2


Area of triangle OAB = * (12)2


=


= 36 cm2


Area of circle = πr2


= * 6 * 6


= cm2


Area of shaded region = Area of ΔOAB + Area of circle - Area of sector OCDE


= -


= (36 + ) cm2


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