Question

The area of an equilateral triangle is 9√3 cm2. Taking each angular point as centre, circle is drawn with radius equal to half the length of the side of the triangle. Find the area of triangle not included in the circles. [Take √3=1.73] a) 1.43 cm2 b) 1.33 cm2 c) 1.23 cm2 d) 1.13 cm2​

Answer 1

Answer:

answer in the attachment

Answer 2

Solution :-

Let us assume that, each side of given equilateral triangle is a cm and radius of circle is equal to r cm .

So,

→ Area of equilateral ∆ = (√3/4)a²

→ (√3/4)a² = 9√3

→ a² = 9 * 4

→ a² = 36

→ a = 6 cm

then,

→ Radius of circle = r = Half of the length of the side of equilateral ∆ = 6/2 = 3 cm .

Since each angle in an equilateral ∆ is equal to 60° . Then, angle at centre is equal to 60°

therefore,

→ Area of sector formed at each angular point = (Angle at centre) * πr²

→ Area of three sectors formed at each angular point = 3 * (60°/360°) * 3.14 * 3 * 3

→ Area of three sectors formed at each angular point = (1/2) * 3.14 * 9

→ Area of three sectors formed at each angular point = 14.13 cm²

hence,

→ Required area = Area of equilateral ∆ - Area of three sectors formed at each angular point

→ Required area = 9√3 - 14.13

→ Required area = 9 * 1.73 - 14.13

→ Required area = 15.57 - 14.13

→ Required area = 1.44 ≈ 1.43 cm² (a) (Ans.)

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