The breathing modes of single suspended gold nanoplates have been examined by transient absorption microscopy. These vibrational modes show very high quality factors which means that their frequencies can be accurately measured. Measurements performed before and after removing the organic layer that coats the as synthesized nanoplates show significant increases in frequency, which are consistent with removal of a few nm of organic material from the nanoplate surface. Experiments were also performed after depositing polymer beads on the sample. These measurements show a decrease in frequency in the region of the beads. This implies that adding a localized mass to the nanoplate hybridizes the vibrational normal modes, creating a new breathing mode which has a maximum amplitude at the bead. The nanoplate resonators have a mass sensing detection limit of ca. 10 attograms, which is comparable to the best results that have been achieved with plasmonic nanoparticles.