What is the area of the marked region?



The marked region is contained in the medium-sized semicircle.
It is the complement of the small semicircle.
The medium-sized semicircle has radius \(\dfrac{1}{2}\), so it has area \(\dfrac{\pi}{8}\).
The small semicircle has area \(\dfrac{\pi}{32}\),see .
So the area of the marked region is \[\dfrac{\pi}{8}-\dfrac{\pi}{32} = \dfrac{3}{32}\pi\,.\]