We present Extreme Ultraviolet Explorer (EUVE) spectroscopy and photometry of the nearby F8 V star HD 35850 (HR 1817). The EUVE short-wavelength 75-175 A and medium-wavelength 160-365 A spectra reveal 28 emission lines from Fe IX and Fe XV to Fe XXIV. The Fe XXI λλ102, 129 ratio yields an upper limit for the coronal electron density, logne<11.6 cm−3. The EUVE short-wavelength spectrum shows a small but clearly detectable continuum. The 75-150 A line-to-continuum ratio indicates approximately solar Fe abundances, with 0.8<Z<1.6 (90% confidence interval). Upper limits have been derived for a dozen high-emissivity Fe X through Fe XIV lines. The resulting emission measure distribution is characterized by two broad temperature components at logT of 6.8 and 7.4. Over the course of the 1 week observation, large-amplitude, long-duration flares were not seen in the EUVE Deep Survey light curve, although the light curve does show signs of persistent, low-level flaring and possible rotational modulation. The EUVE spectra have been compared with nonsimultaneous ASCA SIS spectra of HD 35850 obtained in 1995. The SPEX DEM analysis of the SIS spectrum indicates the same temperature distribution as the EUVE DEM analysis. However, the SIS spectra suggest subsolar abundances, 0.34<Z<0.81. Although some of the discrepancy may be the result of incomplete X-ray line lists, we cannot explain the disagreement between the EUVE line-to-continuum ratio and the ASCA-derived Fe abundance. The X-ray surface flux on HD 35850 is comparable to that of cooler dwarfs of comparable age and rotation like EK Draconis (G0 V) and AB Doradus (K1 V). Given its youth (t≈100 Myr), its rapid rotation (vsini≈50 km s−1), and its high X-ray activity (LX≈1.5×1030 ergs s−1), HD 35850 may represent an activity extremum for single, main-sequence F-type stars. The variability and emission measure distribution can be reconstructed using the continuous flaring model of Gudel provided that the flare distribution has a power-law index α≈1.8. Similar results obtained for other young solar analogs suggest that continuous flaring is a viable coronal heating mechanism on rapidly rotating, late-type, main-sequence stars.