In wireless mesh networks based on IEEE 802.16 WiMAX, each mesh node has its own service area that provides wireless Internet access service to client terminals. The network performance degrades due to radio interference when multiple service areas overlap with each other. To avoid this problem, information of the exact location and size of the service area of neighboring mesh nodes is useful for each mesh node to determine its own service area size. However, the availability of the information depends on the topology construction procedure. In this paper, we discuss a method to determine the size of service areas using the information obtained in topology construction based on IEEE 802.16 WiMAX. Specifically, each mesh node estimates the distance to the nearest neighboring node, and sets the service area size based on this distance. Through performance evaluation, we confirm that our method can increase the size of a single-covered area by an average of 32% compared with the existing method, which is the constant service radius, and can reduce the maximum number of overlapped service areas by approximately 50%.