In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design (shaded region).


Radius (r) of circle = 32 cm


AD is the median of triangle ABC


AO = AD = 32


AD = 48 cm


In triangle ABD,


AB2 = AD2 + BD2


AB2 = (48)2 + (AB/2)2


= (48)2


AB =


=


= 32√3 cm


Area of equilateral triangle, ABC = * (32√3)2


= * 32 * 32 * 3


= 96 * 8 * √3


= 768√3 cm2


Area of design = Area of circle - Area of ΔABC


= ( - 768√3) cm2


 

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