You have an equilateral triangle with sides of length 2. If you drop a perpendicular from one vertex of the triangle to the opposite side, you divide the triangle into two right triangles with hypotenuse 2 and one leg 1. You can use the Pythagorean theorem to determine that , , : the other leg has length , the altitude of the triangle. From that you can calculate the area of the triangle.

Each of the three circles has radius 1 and so area . Each angle of the triangle is 60 degrees which is 60/360= 1/6 of the complete circle. That is, each of the sectors of a circle has area .

The shaded area is the area of triangle minus the three sector areas.