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Travelling long distances to access public service facilities is costly and time consuming, especially to those who suffer the burden of poverty and deprivation. Assessing accessibility based on route-based distances does not work well in rural areas of Africa where people often travel along footpaths and dirt roads (in and out of vehicles) that are not mapped, not necessarily well-defined, could vary based on the season or change over short periods of time. The South African government therefore recommended that geographic accessibility be assessed based on a road network that is augmented by connecting communities to the main road network via a triangulated irregular network (TIN). While this method is recommended, a study about its suitability has not been published. We do this by describing an implementation, analysing the results and comparing these to other techniques. In this paper we present and compare the recommended method to geographic accessibility results of two other frequently used distance measuring techniques: 1) straight-line distances; 2) route-based distances in the road network. We applied the techniques to South African Police Service stations in the O.R. Tambo District Municipality, Eastern Cape, South Africa, which is characterized by rural villages scattered across the landscape, not connected to the road network and where data for footpaths and dirt roads does not exist. The results confirm that in the absence of a completely mapped travel network, the recommended method is a suitable alternative for measuring geographic accessibility in rural areas of Africa without having to spend time and money on mapping footpaths and dirt roads that keep on changing anyhow. However, the results reveal sensitivity to the threshold distance and significant local variation depending on distance from urban areas and proximity to natural barriers such as rivers. The latter must be considered when deciding whether to apply the recommended distance measurement technique in rural accessibility studies. Further research could compare the techniques for other study areas and also refine the method, e.g., by experimenting with different algorithms for centroids of populated areas and finding ways to estimate travel speeds on TIN arcs. [ABSTRACT FROM AUTHOR]