What is the area of the marked region?



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