The circle bisects each side of the triangle, so the line length of the shadow part of the circle is 2, and the shadow part of the triangle just forms an equilateral triangle with a side length of 2 (it is also conceivable that the circle rotates 60).

The shaded part is the sum of the areas of three equilateral triangles with two sides.

So it is easy to calculate the total area =3*(2*√3)/2=3√3.