Many developmental processes of multicellular organisms involve the patterning and growth of two-dimensional tissues, so called epithelia. We have quantified the growth of the wing imaginal disk, which is the precursor of the adult wing, of the fruit fly Drosophila melanogaster. We find that growth follows a simple rule with exponentially decreasing area growth rate. Anisotropies of growth can be precisely determined by comparing experimental results to a continuum theory. Growth anisotropies are to good approximation constant in space and time. They are weak in wild-type wing disks but threefold increased in GFP-Dpp disks in which the morphogen Dpp is overexpressed. Our findings indicate that morphogens such as Dpp control tissue shape via oriented cell divisions that generate anisotropic growth.