Real Dictionary

drape
verb: If someone or something is draped in a piece of cloth, they are loosely covered by it.
verb: If you drape a part of your body somewhere, you lay it there in a relaxed and graceful way.
verb: If you drape a piece of cloth somewhere, you place it there so that it hangs down in a casual and graceful way.

drape in American English
cloth hanging in loose folds, or hanging loosely from the thing that it covers
to cover, hang, or decorate with or as with cloth or clothes in loose folds
to hang or fall in folds, as a garment, cloth, etc.
intransitive verb: to hang, fall, or become arranged in folds, as drapery
noun: a curtain or hanging of heavy fabric and usually considerable length, esp. either of a pair for covering a window and drawn open and shut horizontally
transitive verb: to cover or hang with cloth or other fabric, esp. in graceful folds; adorn with drapery

drape in British English
noun: a cloth or hanging that covers something in folds; drapery
verb: to hang or cover with flexible material or fabric, usually in folds; adorn