What is the area of the marked quadrilateral?



The marked quadrilateral is symmetric at the square diagonal that crosses it, so it is a kite.
The symmetry axis cuts the kite into two right triangles.
Their base has length \(\dfrac{1}{2}\), see . Their height has length \(\dfrac{2-\sqrt{3}}{2}\), see .

So the area of the kite is \[\dfrac{2-\sqrt{3}}{4}\,.\]