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Published online by Cambridge University Press: 01 July 2016
We study the contribution made by three or four points to certain areas associated with a typical polygon in a Voronoi tessellation of a planar Poisson process. We obtain some new results about moments and distributions and give simple proofs of some known results. We also use Robbins' formula to obtain the first three moments of the area of a typical polygon and hence the variance of the area of the polygon covering the origin.