  We consider polygonal tilings of certain regions and use these to give
intuitive definitions of tiling-based perimeter and area. We apply these
definitions to rhombic tilings of Elnitsky polygons, computing sharp bounds and
average values for perimeter tiles in convex centrally symmetric 2n-gons. These
bounds and values have implications for the combinatorics of reduced
decompositions of permutations. We also classify the permutations whose
polygons gave minimal perimeter, defined in two different ways. We conclude by
looking at some of these questions in the context of domino tilings, giving a
recursive formula and generating function for one family, and describing a
family of minimal-perimeter regions.
