What is the area of the marked region?



By symmetry and we have that the marked region is the complement of an equilateral triangle with side length \(1\) of a region of area \(\dfrac{\pi}{3}-\dfrac{\sqrt{3}}{2}\), see
Hence its area is \[\dfrac{\sqrt{3}}{4} - \dfrac{\pi}{3}+\dfrac{\sqrt{3}}{2} = \dfrac{3\sqrt{3}}{4}-\dfrac{\pi}{3}\,.\]