Is EX2800 WiFi Range Extender compatible with my NetGear Router model R6120

Will it work? sure

Will it make your wifi better? not enough info.

Reason I say that is a stsandard router should be able to cover 1100sq ft without issues. 

so if you're having issues, then you need to determine why. 

1. is it an intererence issue? try changing the wifi channels you're broadcasting on

2. is it a materials issue? what I mean is your home made of brick/concrete/adobe/plaster lathe/or some other materials that block wifi? If so, then adding an extender isn't always going to help. It potentially can but it isn't a for sure. 

3. Is it something in the walls blocking wifi? metal hvac is great at blocking wifi. Sometimes moving a router laterally can help with signal propagation.