The Diels-Alder reactivity of maleic anhydride to the bay regions of planar polycyclic aromatic hydrocarbons has been explored computationally within the Density Functional Theory framework. It is found that the process becomes more and more exothermic and the associated activation barriers become lower and lower when the size of the system increases. This enhanced reactivity follows an exponential behavior reaching its maximum for systems having 18-20 benzenoid rings in their structures. This peculiar behavior has been analyzed in detail using the activation strain model of reactivity in combination with the energy decomposition analysis method. In addition, the influence of the change in the aromaticity strength of the polycyclic compound during the process on the respective activation barriers has been also studied