The Pink Area

We can combine the 3 circular sectors to obtain a circular sector of radius 1 and central angle $60 ^ \circ + 60 ^\circ + 60^\circ = 180^\circ$ . This is a semicircle which has area $\frac{1}{2} \times \pi \times 1^2 = \frac{ \pi}{2}$ .

The equilateral triangle has a base of 2, and a height of $\sqrt{3}$ , so it has an area of $\frac{1}{2} \times 2 \times \sqrt{3} = \sqrt{3}$ .

Since the purple area is equal to the equilateral triangle minus the circular sectors, it has an area of $\sqrt{3} - \frac{\pi}{2}$ .