In a circular table corner of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. Find the area of the design.

In ΔBOD
By Trigonometry,
BD = 32sin60° = 27.71cm
BC = 55.43cm
OD = 32cos60° = 16cm
∴Area of ΔBOC = 1/2 × 16 × 55.43 = 443.4cm²
∴Area of Equilateral triangle = 3 × Area ΔBOC = 3 × 443.4 = 1330.2cm²
Area of circle = π × r² = 3.14 × 32 × 32 = 3215.36cm²
∴Area of shaded region = 3215.36 - 1330.2 = 1885.16cm²