What is the area of the marked region?



Consider the marked region together with its symmetrical image at the center of the square.
This larger region has twice the area of the marked region.
The larger region is the complement in the square of two quarter circles having each area is \(\dfrac{\pi}{8}\), see .
The area of the marked region is then \[\frac{1}{2}(1-2\cdot \dfrac{\pi}{8})=\dfrac{1}{2}-\dfrac{\pi}{8}\,.\]