@Damngflo 

Hey

Its not possible to say for 100% certain, but I would guess that 1 AP in the centre should cover the 40 x 40 house for you.

In relation to the difference between the 115 and 225.    The 115 is a WiFi4 device (N Grade) and the 225 is WiFi5 (AC Grade).   For clarity WiFi6 is the newest, WiFi5 is the most commonly used and WiFi4 is pretty much end of life now.

Yes there is a jump in price, but honestly I would recommend against choosing the 115 at this stage, its old technology.   The 225 would be the better option for you and should serve you well for a good few years.

In regard to a POE switch, that one is 10/100 ports.. if you are going to change the switch choose a 10/100/1000 (Gigabit Switch), but this is not necessary as the EAP225 will come with a POE injector that you can use to power it.    Save the money on a switch and buy the better AP.

@Damngflo Each EAP can handle 50ft. The main difference between EAP115 and EAP225 is wireless link speed. EAP225 is dual band and supports 5Ghz network, much faster than 2.4Ghz. Also EAP115 only has 100Mbps Ethernet port. 

They do have an article about this: https://www.tp-link.com/us/support/faq/1161/