For any finite collection of pseudodisks in the plane (topological disks whose pairwise intersections are either disks or empty) the area can be computed by inclusion-exclusion as \[ \mu(\bigcup B)=\sum_{\sigma\in\Delta}(-1)^{|\sigma|-1}\mu(\bigcap\sigma), \] where \(\Delta\) is an abstract \(2\)-dimensional nerve complex that can be nicely embedded into the interior of the collection. The proof of the result and the algorithm for the computation of such a nerve complex depends on a topological sweep, and therefore they do not generalize to higher dimensions. The paper contains a nice example of a pseudodisk collection that is not equivalent to a collection of geometric disks. It remains an open problem whether analogous results are valid in higher dimensions, as they are for arrangements of geometric balls, due to \textit{H. Edelsbrunner} [``The union of balls and its dual shape,'' in: ``The László Fejes Tóth Festschrift'' (I. Bárány, J. Pach, eds.), Discrete Comput. Geom. 13, No. 3-4, 415-440 (1995; Zbl 0826.68053)].