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Wireless Sensor Networks (WSNs) consist of a large number of small and low cost sensor nodes powered by small batteries and equipped with various sensing devices. Usually, for many applications, once a WSN is deployed, probably in an inhospitable terrain, it is expected to gather the required data for quite some time, say for years. Since each sensor node has limited energy, these nodes are usually put to sleep to conserve energy, and this helps to prolong the network lifetime. There are two major approaches to sleep scheduling of sensor nodes, viz. (i) random (ii) synchronized. Any sleep scheduling scheme has to ensure that data can always be routed from source to sink. In this paper, we propose a novel approach for sleep scheduling of sensor nodes using a tree and an energy aware routing protocol which is integrated with the proposed sleep scheduling scheme. The tree is rooted at the sink node. The internal nodes of the tree remain awake and the leaf nodes are made to sleep. This provides an assured path from any node to the sink node. The tree is periodically reconstructed considering the remaining energy of each node with a view to balance energy consumption of nodes, and remove any failed nodes from the tree. The proposed approach also considerably reduces average energy consumption rate of each node as we are able to put more number of nodes to sleep in comparison to other approaches. Additional fault-tolerance is provided by keeping two paths from each node towards the sink. Extensive simulation studies of the proposed routing protocol has been carried out using Castalia simulator, and its performance has been compared with that of a routing protocol, called GSP, which incorporates sleep scheduling using random approach. The simulation results show that the proposed approach has longer network lifetime in comparison to that provided by GSP, and the energy consumption of nodes is also balanced.