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  = r2

=  x  x 6 x 6

= cm2

Area of triangle OAB =  x (12)2

= 36 cm2

Area of circle = πr2

=  × 6 × 6

= cm2

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

= -

= (36 + ) cm2

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