We observed two solar active regions (NOAA regions 7563 and 7565), quiet-Sun areas, and a coronal hole region simultaneously with Goddard Space Flight Center's Solar EUV Rocket Telescope and Spectrograph (SERTS) and with the Yohkoh Soft X-ray Telescope (SXT) on 1993 August 17. SERTS provided spatially resolved active region and quiet-Sun slit spectra in the 280 to 420 A wavelength range, and images in the lines of He II λ303.8, Mg IX λ368.1, Fe XV λ284.1, and Fe XVI λλ335.4 and 360.8 SXT provided images through multiple broadband filters in both the full-frame imaging mode and the partial-frame imaging mode. The SERTS images in Fe XV (log Tmax = 6.33, where Tmax is the temperature which maximizes the fractional ion abundance in the available ionization equilibrium calculations, i.e., the formation temperature) and Fe XVI (log Tmax = 6.43) exhibit remarkable morphological similarity to the SXT images. Whereas the Fe XV and XVI images outline the loop structures seen with SXT, the cooler He II (log Tmax = 4.67) and Mg IX (log Tmax = 5.98) images outline loop footpoints. In addition, the Mg IX emission outlines other structures not necessarily associated with the hot loops; these may be cool (T 1 × 106 K) loops. From the spatially resolved slit spectra, we obtained emission-line profiles for lines of He II λ303.8, Mg IX λ368.1, Fe XIII λ348.2, Si XI λ303.3, Fe XIV λ334.2, Fe XV λ284.1, and Fe XVI λ335.4 for each spatial position. Based upon the spatial variations of the line intensities, active region 7563 systematically narrows when viewed with successively hotter lines, and appears narrowest in the broadband soft X-ray emission. The active region width (full width at half-maximum intensity) diminishes linearly with log Tmax; the linear fit yields an extrapolated effective log Tmax of 6.51 ± 0.01 for the X-ray emission. The most intense, central core straddles the magnetic neutral line. Active region and quiet-Sun one-dimensional temperature scans were derived from intensity ratios of spatially resolved SERTS slit spectral lines, and from coregistered SXT filter ratios. The highest plasma temperatures were measured in the most intense, central core of region 7563. The temperatures derived from Fe XVI λ335.4/Fe XV λ284.1 and Fe XVI λ335.4/Fe XIV λ334.2 vary significantly (based upon the measurement uncertainties) but not greatly (factors of less than 1.5) across the slit. The average log T values derived from the above two ratios for region 7563 are 6.39 ± 0.04 and 6.32 ± 0.02, respectively. Somewhat larger systematic variations were obtained from all available SXT filter ratios. The average active region log T values derived from the SXT AlMgMn/thin Al, thick Al/thin Al, and thick Al/AlMgMn filter ratios are 6.33 ± 0.03, 6.45 ± 0.02, and 6.49 ± 0.03, respectively. Active region and quiet-Sun one-dimensional density scans were derived from intensity ratios of spatially resolved SERTS slit spectral lines of Fe XIII and Fe XIV. The derived densities show neither systematic nor significant variations along the slit in either the active region or the quiet-Sun, despite the fact that the intensities themselves vary substantially. This indicates that the product of the volume filling factor and the path length (fΔl) must be greater by factors of 3-5 in the active region core than in the outskirts. Furthermore, the derived active region densities are ~2 times the quiet-Sun densities. This density difference is adequate to explain the factor of ~4 intensity difference in Fe XII and Fe XIII between the active and quiet areas, but it is not adequate to explain the factor of ~8 intensity difference in Fe XIV between the active and quiet areas. We attribute the latter to a greater fΔl in the active regions. Statistically significant Doppler shifts are not detected in region 7563 or in the quiet-Sun with any of the EUV lines.