Area coverage is one of the key issues for wireless sensor networks. It aims at selecting a minimum number of sensor nodes to cover the whole sensing region and maximizing the lifetime of the network. In this paper, we discuss the energy-efficient area coverage problem considering boundary effects in a new perspective, that is, transforming the area coverage problem to the target coverage problem and then achieving full area coverage by covering all the targets in the converted target coverage problem. Thus, the coverage of every point in the sensing region is transformed to the coverage of a fraction of targets. Two schemes for the converted target coverage are proposed, which can generate cover sets covering all the targets. The network constructed by sensor nodes in the cover set is proved to be connected. Compared with the previous algorithms, simulation results show that the proposed algorithm can prolong the lifetime of the network.