  We have investigated the doping dependencies of the basal areas in
single-layer high-T_c cuprates La_{2-x}Sr_xCuO_4 and HgBa_2CuO_x, as well as in
two-layer Y_{1-y}Ca_yBa_2Cu_3O_x and HgBa_2CaCu_2O_x. The basal areas not only
tend to shrink on hole doping, as expected from single electron quantum
chemistry, but exhibit also a "bulge'' around optimum doping. We attribute the
"bulge'' to the effects of the strongly correlated quantum liquid on the CuO_2
lattice, rendering it nearly incompressible around optimum doping, but highly
compressible in the weakly overdoped regime. Inhomogenous doping cannot account
for this anomaly in the electronic compressibility of the CuO_2 lattice.
