  We prove that the (n-2)-dimensional surface area (perimeter) of central
hyperplane sections of the n-dimensional unit cube is maximal for the
hyperplane perpendicular to the vector (1,1,0,...,0). This gives a positive
answer to a question of Pelczynski who solved the three dimensional case. We
study both the real and the complex versions of this problem. We also use our
result to show that the answer to an analogue of the Busemann-Petty problem for
the surface area is negative in dimensions 14 and higher.
