A new set of radiative and electron collisional data for Fe XII was presented in two earlier papers. In the present work, we derive level populations and theoretical line intensities for a range of plasma densities and temperatures. Observations of Fe XII lines obtained with the Solar EUV Rocket Telescope and Spectrograph are analysed both as a check on the quality of the new atomic data and to determine the electron density in active regions and the quiet Sun. The discrepancy between the electron density values determined from Fe XII line intensity ratios and those obtained from other ions is investigated.