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# Question

# Answer

4 = (2/3) x height of the triangle

height of triangle = 6

Let the length of one side of the equilateral triangle be 2a.

Using Pythagoras ‘ theorem,

a^2 + 2^2 = 4^2

a = sqrt 12

2a = 2(sqrt 12)

area of triangle = (1/2) x 2(sqrt 12) x 6 = 6(sqrt 12)

area of circle = pi x 2 x 2 = 4pi

area of shaded part = [6(sqrt 12) – 4pi]/3 = **2(sqrt 12) – (4pi/3)**

Ans : * 2(sqrt 12) – (4pi/3) sq cm*.

If you don’t want to use Pythagoras’ Theorem, then you will need to use similar triangles to find the side of the equilateral triangle

Assuming the question is correct,

Height of triangle = 3/2 of diameter of circle = 6 cm

Let the length of the equilateral triangle be 2x cm.

Using Pythagaros’ Theorem,

4x^{2} = x^{2} + 36

3x^{2} = 36

x = 2 √ 3

Length of equilateral triangle = 4√ 3 cm

Area of equilateral triangle = 1/2 x 4√ 3 x 6 = 12√ 3 cm^{2}

Area of circle = 4π

Shaded area = 1/3 (12√ 3 – 4π) cm^{2} = 4√ 3 – 4/3π cm^{2}

Is it really height of the triangle?? If it’s the side, you can get it without square root.

Height : 2*sqrt(12) – 3/4Pi

If it’s a Side : 6 – 3/4Pi

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