Q:

What is the area of $PXQY$ in the rectangle $ABCD$ in the following diagram?

In $ABCD$ rectangle $AB=6$, $AD=8$, $AE=ED$, $BF=FC$, $EP=PQ=QF$. Find
  the area of $PXQY$.

Source: Bangladesh Math Olympiad 2014 Junior Category
I cant prove that which type of quadrilateral it is. How can I get the diagonal or the sides of $PQXY$? Please help me with a hint. 

A:

$PF=FC$ and $PF\perp FC,$ which says $$\measuredangle QPY=\measuredangle FPC=45^{\circ},$$
which gives that $PXQY$ is a square and
$$S_{PXQY}=\frac{XY\cdot PQ}{2}=\frac{2^2}{2}=2.$$

