What is the area of the marked region?



The marked region is contained in a region with area \(1-\dfrac{\sqrt{3}}{4}-\dfrac{\pi}{6}\) , see .
It is half of the complement of a circle of area \(\dfrac{\pi}{256}\), see , and a region of area \[\frac{15}{32} - \frac{\sqrt{3}}{4} - \frac{\pi}{6} + \frac{255}{256}\arcsin\!\left(\frac{8}{17}\right)\,,\] see .
We deduce that the area of the marked region is \[ \frac{17}{64} -\frac{\pi}{512} -\frac{255}{512}\arcsin\!\left(\frac{8}{17}\right) \,. \]