Calculating Antenna Gain
In many antenna designs, such as a dipole, the physical aperture has no direct correlation to directivity and therefore gain of the antenna. For example, a 1/2 wavelength dipole has a gain of 1.65 while an extremely short dipole, say 0.05 wavelengths long, has a gain of 1.5 at the same frequency. You may not be able to effectively drive the short dipole but its directivity is nearly the same. 

So I hope you can see that your premise of starting with the physical aperture is the wrong approach. In fact, no receive antenna can have current induced in it by a plane wave that is more than about 0.16 wavelengths away. You may find it helpful to study Effective Aperture, directivity, and efficiency. A classic book in this field was written by John Kraus. You may also find some suitable texts published by ARRL.