A new analytical theory has been developed for the thermodynamics of dilute-to-moderately concentrated solutions of rigid plates of arbitrary dimensions. The approach presented differs from most current theories by allowing for a continuous distribution of plate orientations rather than a small set of discrete orientations. With a few simple approximations, the theory is made tractable enough to allow for the straightforward determination of the thermodynamic properties. The results of the theory, which contains no adjustable parameters, are in good agreement with the results of Monte Carlo simulations of spatially sparse distributions of plates created by random sequential addition. An example set of the free energy of mixing curves and a phase diagram are also presented, and the prospects for future development of the theory are briefly discussed.