kaĝo

A cage is not an age. Kaĝo ends in the same three letters as aĝo, age, and the resemblance catches beginners in dictation more often than it has any right to. There is no suffix at work here. Aĝ- is a root, not an affix - Esperanto has -aĵ- for a concrete thing and no -aĝ- at all - and even if it were one, there is no root k- for it to attach to. Kaĝ- is a single borrowed unit and the hat is part of it.

Where the hat comes from. French cage is pronounced with the sound Esperanto writes ĝ, and that is what Zamenhof took: the French sound rather than the Latin spelling. Do the same with paĝo (page), aĝo, vojaĝo (journey) and etaĝo (storey) and a pattern appears - French words in -age and -ge come into Esperanto with ĝ. The trap is that this makes them all look like they end in a suffix, and none of them does.

The Latin behind it is a small gift. Cavea was a hollow, then a coop, then the animal pens under a Roman amphitheatre. Its diminutive caveola went through Old North French as gaiole and became English gaol and jail. So a birdcage and a prison are etymological twins, which is exactly the metaphor every writer reaches for anyway. In Esperanto the metaphor is live too: enkaĝigi is to cage something, elkaĝigi to let it out, and kaĝbirdo is a cagebird.