Dutch Mathematical Olympiad

In the left square, rectangle $ABFE$ is drawn. In the right square, rectangle $PSRQ$ is drawn, where the sides $QR$ and $PS$ are parallel to the diagonal $AC$ of the square. The sides of both squares have length $6$. It turns out that the rectangles $ABFE$ and $PSRQ$ have exactly the same dimensions.



What is the length of $AE$?