Case Fan Sizes Confusion

hi, ok i just need something to be cleared up. I have this rear exhaust hole right. it measures ~3.5" by 3.5". i have no idea what size fan would fit this. 2 sources told me to measure DIAGNALLY but how does that make sense when case fan specs are give like 80x80x35? also he told me i needed a 120mm case fan (computer customer service). 120mm specs are 120mmX120mm and 120 is about 4.5inchs. so i have no idea how this would fit. he just said "it may not look like it will fit, but it will".

one more thing. i have a 70mm fan on my cpu. it's getting kind loud so i need it replaced. however theyre more expensive than 80mms. so i was thinkn about an adapter. but the problem is the 70mm fan is kind of clipped on to the heatsink and the adapter i dont think will work like this.
fan adapter link: http://svc.com/fa7080-uvblu.html

yeah.. and if i really do need a 120mm case fan, anyone know any quiet or even silent ones out there?