For a $N$-element planar phased array, all the elements are same isotropic antennas. Then, what is the effective area of this array? Is it $$A_e=\frac{\lambda^2}{4\pi}GN$$ where $G$ is the directivity of a fixed angle $(\theta,\phi)$.

Meanwhile, as the antennas are isotropic, is the beamforming cause the $G$ times change in effective area?