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,

AB^{2} = AD^{2} + BD^{2}

AB^{2} = (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 cm^{2}

Area of design = Area of circle - Area of ΔABC

= ( - 768√3) cm^{2}

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