What is the area of the marked region?



The marked region is the overlap of two quarters of circle.
Each quarter of circle has area \(\dfrac{\pi}{4}\).
The union of the two quarter of circles is the full square, which has area \(1\).
The area of the marked region is then \[2\cdot \dfrac{\pi}{4}-1=\dfrac{\pi}{2} - 1\,.\]