This paper details work done by the authors at the Hope College Research Experiences for Undergraduates Site in Summer 1999.
Abstract: In this article, we explore ways of generating triangles randomly if the perimeter is a fixed real number. The methods studied involve putting a polynomial joint probability density function on the space of triples (A,B,C) of possible side lengths. We derive formulas for the mean area (and for the higher moments of the area) in each case.
This article appeared in Pi Mu Epsilon Journal, 11, No. 7, 2002, pp. 365-371.