  The total diameter of a closed planar curve $C\subset R^2$ is the integral of
its antipodal chord lengths. We show that this quantity is bounded below by
twice the area of $C$. Furthermore, when $C$ is convex or centrally symmetric,
the lower bound is twice as large. Both inequalities are sharp and the equality
holds in the convex case only when $C$ is a circle. We also generalize these
results to $m$ dimensional submanifolds of $R^n$, where the "area" will be
defined in terms of the mod $2$ winding numbers of the submanifold about the
$n-m-1$ dimensional affine subspaces of $R^n$.
