The atomically thin two-dimensional (2D) materials have received remarkable attention for their promising applications in cutting-edge technological applications. In this article, we devised square and hexagonal shaped monolayers from the 110-facet and 011-facet of beta-BeO type structured ZnO by separating them from the adjacent layers by a distance of 20 angstrom. The energetic stability, lattice parameters, electronic and optical properties of these monolayers have been examined comprehensively using the density functional theory. In pursuit of this study, the wurtzite structured ZnO (w-ZnO) is first transformed into the beta-BeO structure by applying a negative pressure of-5.4 GPa. The obtained monolayers exhibited comparable cohesive and formation energy to that of w-ZnO. The electronic structure calculations performed with the Tran-Blaha modified Becke Johnson exchange potential, demonstrated the 110-monolayer as indirect bandgap and 011-monolayer as direct bandgap semiconductors having bandgaps 1.59 eV and 1.72 eV respectively. The 110-monolayer exhibited isotropic optical coefficients whereas considerable anisotropy has been recorded in the dispersion of optical spectra of 011-monolayer. Also, these monolayers exhibited thermally stable excitons of binding energies estimated as 3.32 eV for 110-monolayer and 1.53 eV along the x-axis and 1.19 eV along the y-axis for 011-monolayer. Investigations of the refractive indices indicated both monolayers as of transparent nature. Our study provides the pathways to serve as a useful reference for designing low-cost and nontoxic 2D polymorphs of ZnO for optoelectronic applications in miniaturized portable devices.