  The discrete isoperimetric inequality in Euclidean geometry states that among
all $n$-gons having a fixed perimeter $p$, the one with the largest area is the
regular $n$-gon. The statement is true in spherical geometry and hyperbolic
geometry as well.
  In this paper, we generalize the discrete isoperimetric inequality to
disconnected regions, i.e. we allow the area to be split between regions. We
give necessary and sufficient conditions for the result (in Euclidean,
spherical and hyperbolic geometry) to hold for multiple $n$-gons whose areas
add up.
