'flat-roofed' is a compound formed from 'flat' + 'roofed'. 'flat' originates from Old Norse, specifically the word 'flatr', where 'flatr' meant 'broad, flat'; 'roof' originates from Old English, specifically the word 'hrof'; the suffix '-ed' forms adjectival (past-participial) forms in English.

'flat' entered Middle English via Old Norse 'flatr' and developed into modern English 'flat'; 'roof' developed from Old English 'hrof' to Middle English 'roof'; the compound adjective 'flat-roofed' arose in modern English as a straightforward descriptive formation.

Initially it literally combined the senses of 'flat' and 'roof' to describe something 'having a flat roof'; this basic descriptive meaning has remained stable into modern usage.