CONO-SUR 2014 Problem 3

Let $ABCD$ be a rectangle and $P$ a point outside of it such that $\angle{BPC} = 90^{\circ}$ and the area of the pentagon $ABPCD$ is equal to $AB^{2}$ .

Show that $ABPCD$ can be divided in 3 pieces with straight cuts in such a way that a square can be built using those 3 pieces, without leaving any holes or placing pieces on top of each other.

Note: the pieces can be rotated and flipped over.