mono-stereo Hugo and Amps each have half a square cheese cake. Hugo suggests that Amps shares his cake with his sister Anne, Anne’s mother’s husband and his husbands cat.
Anne cuts each slice to have the same amount of cake, using the perimeter of the cake. (It’s essentially the same as dividing a circular cake into five slices). Since the perimeter of the cake is 20 units (as marked by Hugo’s brother, Alan), then each of the five slices must have 4 units of edge. So, we choose a point on the perimeter and then mark all the other points four units along before shoving it up Alan’s ringer.
As an aside, that would be an incredibly daft method - If at the end you’d have tried to slice from the marked points on the perimeter to the centre of the cake, or the centre to the marked points on the perimeter, you wouldn’t end up with 5 equal slices (as unlike a circular cake you’ve got irregular corners to contend with). And figuring out to what points in the middle of the cake to cut each slice to would be even more of a pain in the arse than Alan would have experienced in your story!
Anne the daft sod needed to have only measured the base of the cake, divided by 5, and sliced vertically.