The compound adjective "wide-brimmed" is a transparent descriptive formation from two native English elements. "Wide" originates from the Old English wīd, a common Germanic term for spatial breadth. "Brim" comes from Middle English brimme, likely related to the edge of the sea or a river, which was later applied to the projecting rim of a hat. The suffix -ed is added to nouns to create adjectives denoting possession of a quality, here forming "brimmed" to mean "having a brim". The logical combination directly describes a hat possessing a brim that is broad from side to side, offering shade or protection.

Structure: wide (broad) + brimmed (having a brim) - wide: From Old English wīd (spacious, broad). An adjective describing a large extent from side to side. - brimmed: From the noun brim (the projecting edge around a hat) + the suffix -med, a variant of -ed used to form adjectives meaning "having or provided with (a specified thing)".