Voronoi Diagram composed of $n$ randomly distributed points

Question

I've been curious about the distributions of the areas of cells in Voronoi diagrams. Say $n$ points are drawn from $\text{Unif}([0,1]\times [0,1])$, and a Voronoi diagram is constructed on the unit square. If $A(n)$ is the random variable describing the area of a random cell, what is it's probability distribution function $f_A(x)$? If there isn't a clean expression for the PDF, can we compute $\text{Var}(A(n))$? I know that $E(A(n)) = \frac{1}{n}$ by symmetry, but don't know if we can make a similar argument for the variance. Any thoughts or advice would be much appreciated!