What is the area of the marked region?



The marked region is contained in a region with area \(1-\dfrac{\pi}{4}\), see .
It can be obtain from it by subtracting two regions with area \(1-\dfrac{\sqrt{3}}{4}-\dfrac{\pi}{6}\), see .
The area of the marked region is then \[1-\dfrac{\pi}{4}-2\cdot (1-\dfrac{\sqrt{3}}{4}-\dfrac{\pi}{6})=\dfrac{\sqrt{3}}{2}+\dfrac{\pi}{12} -1\,.\]