Examples of pairs of ordered congruent-like n-gons with different areas

TL;DR

This paper constructs pairs of articulated n-gons with matching ordered internal angles but different areas for all n>5, highlighting geometric properties of congruent-like polygons.

Contribution

It provides explicit examples of such polygon pairs for all n>5, expanding understanding of angle-area relationships in articulated polygons.

Findings

Pairs of n-gons with same internal angle sequences but different areas exist for all n>5.

The examples demonstrate that angle congruence does not imply equal area in articulated polygons.

This work extends geometric knowledge on polygon congruence and area variation.

Abstract

In this Paper, for every $n>5$, we show examples of pairs articulated $n$-gons $P$ and $P'$ of different area such that every ordered sequence of internal angles of $P$ coincide with some ordered sequence of internal angles of $P'$.