Brim
Brim is the upper edge or projecting part of a hat, often designed to provide shade or protection from the elements. It can vary in size and shape depending on the style of the hat, such as a wide brim for sun hats or a narrow brim for fedoras.
In addition to hats, the term "brim" can also refer to the edge of a container, like a cup or bowl. For example, when filling a glass, one might fill it to the brim, meaning it is full to the top without overflowing.