We provide a derivation of the Föppl-von Kármán equations for the shape of and stresses
in an elastic plate with incompatible or residual strains. These might arise from a range
of causes: inhomogeneous growth, plastic deformation, swelling or shrinkage driven by
solvent absorption. Our analysis gives rigorous bounds on the convergence of the threedimensional equations of elasticity to the low-dimensional description embodied in the
plate-like description of laminae and thus justifies a recent formulation of the problem to
the shape of growing leaves. It also formalizes a procedure that can be used to derive other
low-dimensional descriptions of active materials with complex non-Euclidean geometries