One major challenge of studying extensive air showers (EAS) from cosmic rays with energy $>$1TeV lies in the measurement of the muon content in EAS, even though muon detectors have been deployed among various ground-based EAS experiments. There are many benefits from the measurement of muon content over several orders of magnitude in energy, such as mass composition analysis, gamma/hadron discrimination, testing hadronic interaction models, and even primary energy reconstruction. However, the stochastic nature of hadronic interaction processes introduces significant fluctuations in the muon component of EAS, which is an obstacle to comprehensive EAS physics. Thus, it is essential to construct muon detectors with dense coverage while also sampling shower particles with very wide coverage ($\sim$ 1 km$^2$). In this regard, the Large High Altitude Air Shower Observatory (LHAASO) could help to accurately measure the muon content for showers from cosmic rays with energies from tens of TeV to tens of PeV with the Kilometer Square Array (KM2A), which is equipped with over 40,000 m$^2$ muon detectors (MDs) ($\sim4.4\%$ coverage). In addition, LHAASO provides an opportunity to measure the muon component using an adjacent homogeneous detector with full coverage over 78,000 m$^2$, the Water Cherenkov Detector Array (WCDA). This work explores the potential of an unburied water-Cherenkov detector array as a muon counter to measure muon content in EASs with LHAASO KM2A-WCDA synergy.