Understanding the response of atmospheric blocking events to climate change has been of great interest in recent years. However, potential changes in the area (size) of blocking events, which can affect the spatio-temporal characteristics of the resulting extreme events, have not received much attention. Using two large-ensemble, fully-coupled GCM simulations and two blocking indices, we show that the size of blocking events increases with climate change, particularly in summers of the northern hemisphere (by as much as 17%). Using a two-layer quasi-geostrophic model and a dimensional analysis technique, we derive a scaling law for the size of blocking events, which shows that area mostly scales with the width of the jet times the Kuo scale (i.e., the length of stationary Rossby waves). The scaling law is validated in a range of idealized GCM simulations. This scaling's predictions agree well with changes in blocking events' size under climate change in fully-coupled GCMs in winters but not in summers. The results suggest that future studies should focus on investigating the consequences of larger blocks on the size, magnitude, and persistence of extreme weather events, and on improving the understanding of summer blocks.