No single access point with will reliably cover 4000 sqm (let alone 4km^2) without dead zones, they are simply not powerful enough.
The range of an AP device depends on a large number of external factors like walls (and what they are made of) and other obstacles as well as the sensitivity of the antenna, the number of antenna and the protocol (802.11n will far outperform 802.11g) as well as frequency (2.4 gig band goes much further then 5 gig band - especially indoors, but has more noise issues - while few devices support 5 gig band). You also need to bear in mind how heavily it will be used - lots of users will substantially decrease effective range.
You will probably need to deploy multiple AP's on the same ESSID with different non-overlapping channels. You will also want either access points with "guest" functionality or 2 sets of access points for the indoor area.
According to this link 802.11g has a radius of approx 46 meters indoors and 92 meters outdoors. You can probably get twice the radius with MIMO enabled 802.11n devices.
As you are going to need to link multiple devices, you may want to get dual band AP's with directional antennas on the 5 gig band as well as 2.4 gig. (You will need to work out how you are going to connect the AP's together).
From the question you ask, I wonder if you might be better off getting a company which specialises in networking to do this for you - doing this properly certainly requires specialist networking knowledge.