Equivalent isoperimetric figures, pentominoes, and geoboard

Abstract

This article presents an investigation into strategies for constructing isoperimetric polygonal figures (those with the same perimeter) and equivalent figures (those with the same area), based on elements of recreational and manipulative geometry. The objective is to use the properties of isoperimetry and equivalence of polyominoes, particularly pentominoes, in combination with the geoboard as didactic tools for constructing isoperimetric and equivalent polygonal figures. The study adopts a methodological approach grounded in a theoretical essay, with potential applicability in teaching and learning contexts. This approach is pedagogically valuable, as it enables a deeper understanding of the mechanisms involved in designing such representations and their educational function. The results indicate that the integration of pentominoes and the geoboard constitutes an effective didactic strategy for teaching and learning geometric concepts, promoting visualization, comparison, and analysis of metric properties of plane figures.