This paper introduces an alternative statistical geometrical method for the evaluation of the thermodynamic properties of hard-particle systems. We develop a general theory which allows one to express average quantities in terms of geometrical "measurables." The theory is tested with the known exact results for the one-dimensional hard rod fluid. We also discuss the potential benefits of the theory in efficiently calculating the chemical potential and pressure (using Monte Carlo methods) of dense hard-particle fluids in two and three dimensions.