SMO 2015 Junior Round 1 Question 31

In the diagram below, $ABCD$ is a trapezium with $\angle D=45^\circ$, $\angle A=90^\circ$, $|BC|=1$ and $|CD|=2\sqrt{2}$. $E$ is a point on $CD$ such that $AE$ is perpendicular to $CD$, find the value of $4|AE|^2$.