膠庄

It seems that you didn't notice the constraint of 0<2k<a, i.e. 0<k<a/2.
This is because "E and F are two points of AD and AB respectively".
Therefore 0<AF<AB, i.e. 0<2k<a.
As a result, k cannot be 3a/4.

The correct answer should possibly be nearly (a^2)/2 with k extremely near a/2 and 2k extremely near a.

Hope this helps