Languages are endlessly fascinating in how one 'false friend' in one language can be the opposite in another!
In German, "Gymnasium" is an academically ambitious high school (one could perhaps even an academy in US English) while in Portuguese an 'academia' means a gymnasium!
Maybe that's a good trick for remembering this one :)
I wonder if they all came from the same origin, in a time where perhaps sports and studies were all together?
- Academia = A workout gym
- Academia = Academy (less often) - Related to academic/scholar issues
- Ginásio = A closed building containing sports courts inside
- Ginásio = High school