The statistical size effect has generally been explained by the weakest-link model, which is valid if the failure of one representative volume element (RVE) of material, corresponding to one link, suffices to cause failure of the whole structure under the controlled load. As shown by the recent formulation of fishnet statistics, this is not the case for some architectured materials, such as nacre, for which one or several microstructural links must fail before reaching the maximum load or the structure strength limit. Such behavior was shown to bring about major safety advantages. Here, we show that it also alters the size effect on the median nominal strength of geometrically scaled rectangular specimens of a diagonally pulled fishnet. To derive the size effect relation, the geometric scaling of a rectangular fishnet is split into separate transverse and longitudinal scalings, for each of which a simple scaling rule for the median strength is established. Proportional combination of both then yields the two-dimensional geometric scaling and its size effect. Furthermore, a method to infer the material failure probability (or strength) distribution from the median size effect obtained from experiments or Monte Carlo simulations is formulated. Compared to the direct estimation of the histogram, which would require more than ten million test repetitions, the size effect method requires only a few (typically about six) tests for each of three or four structure sizes to obtain a tight upper bound on the failure probability distribution. Finally, comparisons of the model predictions and actual histograms are presented.