Area and Volumes of Platonic Solids

Abstract

Platonic solids are five geometric bodies that share a set of similar geometric characteristics. They are also called perfect solids, Platonic polyhedra and cosmic bodies among other names. Platonic solids are regular and convex polyhedra and include: tetrahedron, cube (or hexahedron), octahedron, dodecahedron and icosahedron. This paper presents the mathematical deductions of the formulas for areas and volumes of Platonic solids. The main objective is to demonstrate the geometric analysis to obtain the formulas of areas and volumes, while recognizing that the study of the different techniques and methods of demonstration allow the application of the calculation of areas and volume to the resolution of practical problems that arise in various demonstrative situations of mathematics. It should be noted that these forms of demonstrations are based on the common basic properties of the classical geometric objects of geometry. On the other hand, the concept of area and volume is generalized to several closed figures, thus allowing a greater generality on these concepts to be built through other teaching and learning strategies. Finally, the area and volume formulas are programmed in the high-level programming language Python, using the functional programming paradigm.