In this paper we study the problem of partitioning a convex polygon P of n vertices into m polygons of equal area and perimeter. We give an algorithm for m = 2 that runs in 0(n) time, and an algorithm for m = 2(k), where k is an integer, that runs in O ((2n)(k)) time. These are the first algorithms to solve this problem. (C) 2015 Elsevier B.V. All rights reserved.