The Si(111)-@sr@3x@sr@3-Ag surface can be formed by depositing one monolayer of Ag atoms on a Si(111)-7x7 surface. One of the surface-state bands at this surface provides an ideal two-dimensional system of conduction electrons (2DES). The 2DES is confined in a @sr@3x@sr@3-Ag domain surrounded by atomic steps or out-of-phase boundaries. In this work, we consider a strip domain with finite width and infinite length. By means of the time-dependent local-density approximation, we investigate low-dimensional plasmons (LDPLs) in a metallic strip monolayer on the semiconductor surface, namely, LDPLs in a 2DES confined in a strip region. We analyze the energy-loss intensity, the energy dispersion, and the induced charge distribution of the two plasmon modes at each wave number q along the strip. When wavelength @lambda@ (= 2@pi@/q) of the mode is considerably smaller than the strip width D, the higher-energy mode (HEM) has its induced charges extending widely in an interior region, showing a definite character of the area plasmon (APL). Its energy is quite close to that of the two-dimensional plasmon in an infinite area (pure 2DPL). However, as the mode energy deviates upward from that of the pure 2DPL with increase in @lambda@, the induced charge distribution of the APL evolves into a standing-wave pattern with its free end at the edge. In contrast, the lower-energy mode (LEM) has its induced charges localized near the strip edge, exhibiting a definite character of the edge plasmon. When @lambda@ is small compared with D, the induced charge density of the LEM decays slowly on the inside of the strip owing to the influence of the HEM (APL) close to the LEM in energy. At larger @lambda@ values, the quick attenuation of the induced charge density inside the strip involves conspicuous oscillations due to the interference of electronic waves impinging on and reflected from the edge.