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The activity scheduling of sensors to alternately wake up for sensing obligation such that the network lifetime can be efficiently prolonged is a very important issue in wireless sensor networks (WSNs). Target area coverage is a new coverage problem in wireless sensor networks. The paper addresses the target area coverage problem and schedules sensors to alternatively wake up to collaboratively cover and sense the target area. A geometric-based activity scheduling scheme, named GAS scheme, for WSNs to fully cover a target area is proposed. By means of computational geometry, the sensors can self-determine when to sleep or wake up while preserving the sensing coverage. GAS is able to find as few sensors as possible to cover the target area, which is termed a cover set. In addition, GAS can find as many number of cover sets as possible to be alternately in charge of the sensing task. Simulation results show that GAS can efficiently schedule the sensor when to switch between active and sleep modes. Furthermore, the network lifetime can be prolonged significantly in comparison with the state-of-the-art schemes.