The square ABCD has point M located on side AB and point N on side CD. Lines CM and BN intersect at point U. Lines DM and AN intersect at point V. Determine where points M and N should be placed to maximize the area of MUNV.
I attempted to solve to problem by placing the square at (0,0) and making the square 1x1. I then tried approaching it as a polygon of constraints and found the rules of the lines but this gave me too many variables. Should I use a trig approach instead? I do not see where to begin in this case.