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My native language is Spanish and I have found that the same word means different things in Spanish and Portuguese, but I'll take a crack at this because it makes sense to me.
Spanish "pieza", Portuguese "peça" - Usually refers to a piece that can stand by itself, such as piece or art or piece of furniture. It can also refers to things that are part of larger object or collection composed of items that are usually not the same and can be separated from the whole without causing damage to the item. That sounds complicated but a couple of examples should help. A piece from a board game is a "pieza". A part of car such as the carburetor or the radiator is also a "pieza".
Spanish "pedazo", Portuguese "pedaço" - Refers to something that has been cut from something else. They are pieces of the same thing, maybe different size or shape, but basically the same. A piece of cake is a "pedazo"; also a piece of cheese, meat, etc. In Spanish, we also refer to a "pedazo de papel" (piece of paper), which can refer to scrap paper or a complete sheet that hasn't been cut by the user but came from a stack of identical items.
I hope this helps.
The literal translation here with the article is, The clothes of hers so the article is necessary (and why I think DL should be more strict about it in the optional cases as it's easier to drop it once you understand and are actually using the language, than to try to figure out when and where it can be dropped when there is so much other language acquisition confusion happening – but also because it is less optional in the Portuguese outside of Brazil).