What is the area of the marked region?



The four quarter of circles cover the square hence their overlaps have a total area of \[4 \cdot \frac{\pi}{8}-1\,.\] These overlaps consist in four regions like the marked one hence the requested area is \[\frac{1}{4}\cdot \big(4 \cdot \frac{\pi}{8}-1\big)=\dfrac{\pi}{8}-\frac{1}{4}\,.\]