I too am curious as to the purpose behind this. It seems like a lot of ad-hoc work that doesn’t lead to a unique result. There are lots of other arrangements of rectangles that would fit into the same space as in your illustration and I don’t know how one would choose between them. Packing in ever more and more sounds like an attempt to approximate the area. But if the shape is a face, SketchuUp’s entity info panel will tell you its area already.
So, can you tell us more about what you are really aiming to accompish?
Edit: your explanation posted while I was typing. Thanks for the clarification. Are there rules or best practices for arranging the rectangles? Just any arbitrary suite seems strange.