Does the Heron Proof of Kendall’s Little Theorem Generalize to other Area or Volume Formulae?

This was originally posted 1 day earlier. But there was then a debate about what the truest similarity shape spaces in 1-d were, resulting in the penultimate Figure being updated to reflect this. The review being updated for https://wordpress.com/page/conceptsofshape.space/1225 shall detail this debate, and tabulate each of the distinct conceptualizations’ counterpart of this Figure.