  Using information about the rational cohomology ring of the space of oriented
isometry classes of planar n-gons with specified side lengths, we obtain bounds
for the zero-divisor-cup-length (zcl) of these spaces, which provide lower
bounds for their topological complexity (TC). In many cases our result about
the cohomology ring is complete and we determine the precise zcl. We find that
there will usually be a significant gap between the bounds for TC implied by
zcl and dimensional considerations.
