Areas in space, volumes

Abstract

The area of polyhedral surfaces relies on the definitions and the properties of area of plane figures. Thus, the area of the surface of a rectangular parallelepiped with sides equal to α, β and γ is 2(αβ +βγ +γα), the area of the surface of a cube of size δ is 6δ² and similar calculations give the areas of any polyhedron, by adding the areas of their faces. The area of polyhedra, therefore, is not difficult to calculate and consequently possesses little theoretical interest (see however the exercises below).