  We introduce new combinatorial (bijective) methods that enable us to compute
the average value of three parameters of directed animals of a given area,
including the site perimeter. Our results cover directed animals of any
one-line source on the square lattice and its bounded variants, and we give
counterparts for most of them in the triangular lattices. We thus prove
conjectures by Conway and Le Borgne. The techniques used are based on Viennot's
correspondence between directed animals and heaps of pieces (or elements of a
partially commutative monoid).
