There is a quadrilateral with equal-length for opposite sides but the diagonals are different (and I hope the word parallelogram is correct here), what would be the biggest rectangle I can inscribe, and why?

To put this in practical terms:
Someone cut a board and checked that the opposite sides have equal length. However when checking the diagonals, there are deviations. How to get back to a rectangular shape with minimum area to be cut off?

Note: reassembly is not intended here. If it were, there is a trivial solution that I am not interested in: <https://en.wikipedia.org/wiki/Parallelogram#/media/File:Parallelogram_area_animated.gif>