Areas of totally geodesic surfaces of hyperbolic $3$-orbifolds

The geodesic length spectrum of a complete, finite volume, hyperbolic 3-orbifold M is fundamental invariant the topology via Mostow-Prasad Rigidity. Motivated by this, second author and Reid defined two-dimensional analogue given multiset isometry types totally geodesic, immersed, finite-area surfaces called geometric genus spectrum. They showed that if $M$ arithmetic contains surface, then determines its commensurability class. In this paper we define coarser area set areas in We prove number results quantifying extent to which non-commensurable 3-orbifolds can have arbitrarily large overlaps their sets.