Growth forms of tilings are an interesting invariant of tilings. They are fully understood in the periodic case but there are very few examples in the quasiperiodic case. Here this problem is studied for quasiperiodic tilings obtained by the grid method. It is proven that such tilings have polygonal/polyhedral growth forms that can be obtained as projections of central sections of orthoplexes. Furthermore, properties of the obtained growth forms in 2D and 3D cases are studied. This work contributes to a wider understanding of growth forms which can be used to study coordination numbers of grid tilings and in the calculation of topological densities.