TRILBY' (5 letters) A hat with a brim is a type of headwear that has a wide brim extending from the crown. The two most common types of hats with a brim are the FEDORA and the TRILBY. A FEDORA is a soft felt hat with a brim and indented crown, typically creased lengthwise down the crown and pinched near the front on both sides. A TRILBY is a narrow-brimmed hat with a slightly indented crown, typically made of felt or straw.