This paper presents first simultaneous observations of far ultraviolet (FUV) spectra of discrete and diffuse auroras, together with precipitating electrons measured on the same spacecraft, to emphasize the importance of high-resolution FUV images for accurate estimation of precipitating energy flux in the auroral region. An FUV spectrograph image with similar to 2 km x 3 km resolution show small-scale features were embedded in the auroral arcs. Comparison of peak energies of inverted-V events with the corresponding FUV spectra shows that the observed long band N(2) Lyman-Birge-Hopfield (LBH) emission (long LBH band (LBHL): 160.0-171.5 nm) varied more sensitively to the peak energies compared to the short band. Comparison of the inverted-V structures and their energy fluxes with the LBHL irradiance for similar to 10 km x 10 km regions show they are well correlated for peak energy >2 keV. When the data are averaged over a larger area (70 km x similar to 140 km), on the other hand, the LBHL irradiance becomes less bright for the corresponding electron energy flux due to the contribution from the low-intensity background diffuse aurora produced by secondary electrons. This study demonstrates a reliable relationship between precipitating electron energy flux and LBHL intensity is obtained only if the precipitating region and FUV intensity are locally matched with a scale of less than 10 km corresponding to the size of discrete auroras.