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This equation determines the required antenna area for the specified gain at a given wavelength.
Added after 2 minutes:
The net efficiency n is the product of the aperture taper efficiency na , which depends on the electric field distribution over the antenna aperture (it is the square of the average divided by the average of the square), and the total radiation efficiency n * = Pout/Pin associated with various losses. These losses include spillover, ohmic heating, phase nonuniformity, blockage, surface roughness, and cross polarization. Thus n = na * n *. For a typical antenna, n = 0.55.
I think balaguru thavamani is talking about the coverage area of the signal radiated by the antenna, and NOT the cross-sectional area of the antenna.
Well the coverage area depends on multiple factors, and the gain of antenna is related to the coverage area in indirect manner. Gain of an antenna means the radiated signal will be directed towards the desired coverage area. Comparing to the ideal Isotropic antenna any antenna with directional property will give greater coverage in a given area.
What i think from my knowledge is that Antenna range depend upon
1.Height of Antenna
2.Size of Antenna(large size=> large gain=> long range)
4.time of the day
Of course every antenna have a far field pattern which is 2.D^2/Lamda, and signal attenuates depending upon the attenuation factor and signal strength.
balaguru thavamani, some of the factors have been mentioned by atul_microwaves_antenna like
1. Transmit Power (Pt)
2. Antenna Height
3. Coverage area terrain
But one fact you have to understand is that the term "Antenna Coverage Area" is defined by the Receiver unit's ability to detect tx signal. The area within which a receiver can detect the transmitted signal determines the coverage area for the transmitting antenna.