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 work presents analytical demonstrations of the formula for the area and volume of Platonic solids. The main objective is to show several demonstrative variants of area and volume, while recognizing that the study of the different techniques and methods of demonstration allow the application of the calculation of area 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 Platonic solids. On the other hand, the concept of area and volume is generalized to several closed figures, thus allowing a better understanding of these concepts to be built through other teaching and learning strategies.