What is the area of the marked region?



The marked region is an isosceles triangle because it has a symmetry axis.
It is symmetric at the perpendicular bisector of its side that it has in common with the square.
The triangle basis has length \(1\) and the legs have length \(\dfrac{\sqrt{3}}{3}\), see .

By Pythagoras theorem, the triangle height is \(\dfrac{\sqrt{3}}{6}\).
The area of the marked region is then\[\dfrac{\sqrt{3}}{12}\,.\]