I did not know this property of quadrilaterals proposed me a student. I could not prove to the first attempt but I could do after devoting some time. I want to share it here to see if anyone has any proof different from mine.
In the four vertices of a quadrilateral $ABCD$ whose area is $S$, they are drawn parallel to two rectangular straight lines which determines two rectangles (green in the figure below) whose areas are $R$ and $r$. Prove that $$ R + r = 2S$$
Explanation of parallel lines: The quadrilateral and a pair of orthogonal directions are given. $A$ and $C$ are opposite vertices. For one rectangle, draw "horizontal" lines through $A$ and $C$ and "vertical" lines through $B$ and $D$. For the other rectangle, draw "vertical" lines through $A$ and $C$ and "horizontal" lines through $B$ and $D$.