We investigate depletion interactions near a wall caused by polydisperse silica-coated gibbsite platelets, using total internal reflection fluorescence microscopy (TIRF) to characterize the sphere-wall interaction potential. As no theoretical model for polydisperse platelets exists, we extend a model for monodisperse depletant cylinders by assuming negligible thickness and averaging over the disc size distribution, finding nearly perfect matching with experimental data. The resulting averaged depletion potentials have, as predicted by the extended model, the same depth as monodisperse potentials, but differ in range and shape according to the size distribution. We compare mean particle sizes and standard deviations derived by TIRF with results from TEM measurements.