MathNet 2015-part-01 — 191 problems (EN–VI) Question 161

In the drawing below, $ABCD$ is a rectangle and the points $P$ and $Q$ lie on the diagonal $AC$ so that $AQ = PQ = PC = 1$ and $\angle AQD = \angle BPC = 90^\circ$. Find the area of the rectangle $ABCD$.