'apothem' originates from Greek, specifically the word 'apothemē' (ἀπόθεμα), where the prefix 'apo-' meant 'away' and the root was related to placing or setting (from Greek verbs meaning 'to place').

'apothem' passed into Medieval/Latin geometrical usage (appearing in Late Latin/Medieval Latin forms such as 'apothem(a)') and was adopted into English technical vocabulary as 'apothem'.

Initially related to the general sense of something 'placed away' or 'set off,' but over time it developed the specialized geometric sense of 'the perpendicular from a regular polygon's center to a side.'