We report on the nanometer scale spectral imaging of surface plasmons within individual silver triangular nanoprisms by electron energy loss spectroscopy and on related discrete dipole approximation simulations. A dependence of the energy and intensity of the three detected modes as function of the edge length is clearly identified both experimentally and with simulations. We show that for experimentally available prisms (edge lengths ca. 70 to 300 nm) the energies and intensities of the different modes show a monotonie dependence as function of the aspect ratio of the prisms. For shorter or longer prisms, deviations to this behavior are identified thanks to simulations. These modes have symmetric charge distribution and result from the strong coupling of the upper and lower triangular surfaces. They also form a standing wave in the in-plane direction and are identified as quasistatic short range surface plasmons of different orders as emphasized within a continuum dielectric model. This model explains in simple terms the measured and simulated energy and intensity changes as function of geometric parameters. By providing a unified vision of surface plasmons in platelets, such a model should be useful for engineering of the optical properties of metallic nanoplatelets.