In the diagram, $AB,$ $BC,$ $CD,$ $DE,$ $EF,$ $FG,$ $GH,$ and $HK$ all have length $4,$ and all angles are right angles, with the exception of the angles at $D$ and $F.$


If perpendicular $EM$ is drawn from $E$ to $DF$ (a close-up is shown below), and if $x$ is the length of $EM,$ then what is $x^2$?

Please help with hints! - no solutions -

If u give a full solution I will report u :P
Also, trolls just wanting to get the 50 points will be reported!

Thanks for the help in advance :)