  In this paper we investigate the evolution of the concept of area in Peano's
works, taking into account the main role played by Grassmann's geometric-vector
calculus and Peano's theory on derivative of measures. Geometric (1887) and
bi-vectorial (1888) Peano's approaches to surface area mark the development of
this topic during the first half of the last century. In the sequel we will
present some significative contributions on surface area that are inspired
and/or closely related to Peano's definition.
