What is the area of the marked region?



The marked region is the intersection of two circular sectors.

Each circular sector has area \(\dfrac{\pi}{6}\) because it is one sixth of a circle with radius \(1\).
The union of the two circular sectors consists in two equilateral triangles with side length \(1\).
So it has area \(\dfrac{\sqrt{3}}{2}\).
So the area of the marked region is \[2\cdot \dfrac{\pi}{6} - \dfrac{\sqrt{3}}{2} = \dfrac{\pi}{3}- \dfrac{\sqrt{3}}{2}\,.\]