What is the area of the marked region?



The marked region is a quarter of a circle of radius \(1\) without a region of area \(\dfrac{\pi}{3}-\dfrac{\sqrt{3}}{4}\), see .
Thus the area of the marked region is \[\frac{\pi}{4}-\Big(\dfrac{\pi}{3}-\dfrac{\sqrt{3}}{4}\Big)=\dfrac{\sqrt{3}}{4} - \dfrac{\pi}{12}\,.\]