Why did we do area of shaded region = 2(6 pie- 9* root 3) ???

if you want to find the area of one of the grey shaded region then it will be sector area - area of equilateral triangle

Area of sector = \frac{60}{360}\times \pi\cdot r^2 , \text{where r =6} \tag{1}

Area of equilateral triangle = \frac{\sqrt3}{4}\times \text{s}^2, \text{where side = 6} \tag{2}

From equation 1 and 2 , the area of one of the grey shaded region equals to :

6\pi-9\sqrt{3}

Now, we are ask for the area of two such grey shaded region thus, multiply by 2 or

2\times(6\pi-9\sqrt{3})

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