What is the area of the marked region?



The marked region is the complement in the quarter circle of a semicircle.
The quarter circle has area of \(\dfrac{\pi}{4}\), see .
The semicircle has area \(\dfrac{\pi}{8}\), see .
Thus its area equals \[\dfrac{\pi}{4}-\dfrac{\pi}{8} = \dfrac{\pi}{8}\,.\] REMARK: the area of the marked region is the same as the one of the semicircles.