In this work we present an algorithm that applies segment Voronoi diagrams and planar arrangements to the computation of the metric average of two simple polygons. The idea to apply segment Voronoi diagrams is due to E. Lipovetsky. The implementation of the algorithm is described and a collection of computational examples is presented. Based on the computational framework of the algorithm, the connectedness of the metric average of two simple polygons is studied. Furthermore an artifact produced by the metric average of two simple polygons is identified and a modified averaging operation that avoids this artifact is suggested and implemented. Finally, we extend the algorithm to compute the metric average of two sets that are each a collection of simple polygons with simple polygonal holes.