'asymmetrical-petaled' is a modern English compound formed from 'asymmetrical' and 'petaled'. 'Asymmetrical' ultimately derives from Greek elements 'a-' meaning 'not' and 'symmetria' meaning 'symmetry'. 'Petal' traces back to Greek 'petalon' meaning 'leaf' or 'thin plate' (via Modern Latin 'petalum').

'Asymmetrical' entered English via forms related to Greek 'asymmetria' through Latin/Old French influences and developed into the adjective 'asymmetrical' in modern English; 'petal' entered English in the modern period from Modern Latin 'petalum' < Greek 'petalon'. The compound 'asymmetrical-petaled' is a recent descriptive formation in modern botanical/colloquial English.

Individually, the elements originally meant 'not symmetrical' (asymmetrical) and 'leaf/plate' (petal); combined as a compound they now specifically describe flowers whose petals (shape or arrangement) are not mirror-symmetric.