What is the area of the marked region?



The marked region is the union of two circular sectors with radius \(1\) and angle \(\dfrac{\pi}{3}\).
The area of each circular sector is \(\dfrac{\pi}{3}\).
The intersection of the two circular sectors is a rhombus of area \(\dfrac{\sqrt{3}}{2}\),see .
Hence the area of the marked region is \[\dfrac{2\pi}{3} - \dfrac{\sqrt{3}}{2}\,.\]