  Motivated by the holographic prescriptions for computing entanglement entropy
and complexity, we study the properties of volumes/areas of bulk surfaces. We
obtain a simple formula for the shape dependence of holographic entanglement
entropy in terms of a certain integral over the entangling surface. This easily
generalizes to any bulk codimension-$p$ extremal surface. We study additional
properties of bulk codimension-$p$ extremal surfaces corresponding to
strip/plane "entangling surfaces" in various geometries. We compute universal
terms for codim-one volumes (conjectured to be dual to holographic subregion
complexity) arising from performing relevant deformations. Finally, we describe
several interesting bulk surface constructions which are presumably related to
holographic complexity.
