Partitioning a connected polygon into connected pieces of equal area
To complement Sariel's answer, some closely related problems are hard. In particular, for a non-convex polygon, it's NP-hard to find a partition into two pieces of equal area while minimizing the length of the cut. See: Elias Koutsoupias, Christos Papadimitriou, and Martha Sideri (1992), &quot;On the optimal bisection of a polygon&quot;, ORSA J. Comput. 4 (4): 435–438, doi:10.1287/ijoc.4.4.435.