  We introduce new pseudo-metrics on spaces of Lagrangian submanifolds of a
symplectic manifold $(M,\omega)$ by considering areas associated to projecting
Lagrangian cobordisms in $\mathbb{C} \times M$ to the "time-energy plane"
$\mathbb{C}$. We investigate the non-degeneracy properties of these
pseudo-metrics, reflecting the rigidity and flexibility aspects of Lagrangian
cobordisms.
