Half of a Page, plus

The second sketch inspired by Graham Fletcher's paper cut problem (http://gfletchy.com/paper-cut/). In addition to finding a rectangle that is half the area of the page from which it's cut, he found one where there's a nice dissection of the boundary into the half page. This sketch automates it, sometimes. What is this method? When does it work? Other sketch from this situation: https://tube.geogebra.org/m/2559831