Question

6. 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 design ?​

Answer 1

Solution :-

→ Radius of circular table = 32 cm

so,

→ Area of circular table = πr² = 3.14 * 32 * 32 = 3215.36 cm²

now, since equaliteral ∆ is inside the circle .

then,

→ Radius of circumcircle of a equaliteral ∆ = (a/√3)

→ 32 = (a/√3)

→ a = 32√3 cm .

therefore,

→ Area of equaliteral ∆ = (√3/4) * a² = (√3/4) * (32√3) * (32√3) = 3 * 8 * 32 * √3 = 768 * 1.73 = 1328.64 cm² .

hence,

→ Area of the design = Area of circular table - Area of equaliteral ∆ = 3215.36 - 1328.64 = 1886.72 cm² (Ans.)

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