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We use a fundamental-measure density functional for hard board-like polydisperse particles, in the restricted-orientation approximation, to explain the phase behaviour of platelet colloidal suspensions studied in recent experiments. In particular, we focus our attention on the behavior of the total packing fraction of the mixture, eta, in the region of two-phase isotropic-nematic coexistence as a function of mean aspect ratio, polydispersity, and fraction of total volume gamma occupied by the nematic phase. In our model, platelets are polydisperse in the square section, of side length sigma, but have constant thickness L (and aspect ratio kappa equivalent to L/ < 1, with the mean side length). Good agreement between our theory and recent experiments is obtained by mapping the real system onto an effective one, with excluded volume interactions but with thicker particles (due to the presence of long-ranged repulsive interactions between platelets). The effect of polydispersity in both shape and particle size has been taken into account by using a size distribution function with an effective mean-square deviation that depends on both polydispersities. We also show that the bimodality of the size distribution function is required to correctly describe the huge two-phase coexistence gap and the nonlinearity of the function gamma(eta), two important features that these colloidal suspensions exhibit.