In energy-limited wireless sensor networks, network clustering and sensor scheduling are two efficient techniques for minimizing node energy consumption and maximizing network coverage lifetime. When integrating the two techniques, the challenges include how to decide the most energy-efficient cluster size and how to select cluster heads and active nodes. In this paper, we provide a computation method for the optimal cluster size to minimize the average energy consumption rate per unit area. In the proposed coverage-aware clustering protocol, we define a cost metric that favors those nodes being more energy-redundantly covered as better candidates for cluster heads and select active nodes in a way that tries to emulate the most efficient tessellation for area coverage. Our simulation results validate our computation and show the significant improvement of the network coverage lifetime.