Résumé
L'enseignement mathematique t. 50 (2004) p. 203-237 In this paper we study the area of ideals triangles in a convex domain with
its Hilbert geometry. We obtain a characterization of the hyperbolic geometry
among all the Hilbert geometry in terms of area of ideals triangles. We also
obtain a sharp lower bound on the hilbert area of ideal triangles, independant
of the convex, which characterizes the triangle domains in the plane.
Furthermore, under specific geometric assumptions, we obtain an upper bound,
which depends on the convex domain.