A embalagem do bolo está aberta.

Because de + o contracts to do in Portuguese.

• de = of
• o = the
• de o bolo becomes do bolo = of the cake

This kind of contraction is very common:

• de + a = da
• de + os = dos
• de + as = das

So a embalagem do bolo literally has the structure the packaging of the cake.

Portuguese uses definite articles more often than English.

So where English might say:

• cake packaging
• the cake’s packaging
• the packaging of the cake

Portuguese naturally says:

• a embalagem do bolo

Here:

• a goes with embalagem
• o is part of do and goes with bolo

This sounds normal and natural in Portuguese, even when English might omit one of those articles.

Because estar is used for a state or condition, while ser is usually used for a more permanent characteristic or classification.

In this sentence, aberta means the packaging is currently in an open state, so Portuguese uses estar:

• A embalagem do bolo está aberta. = The cake packaging is open.

If you said é aberta, it would sound like you were describing a general characteristic, which does not fit well here.

A useful shortcut:

• estar + adjective often describes how something is right now
• ser + adjective often describes what something is by nature

Because aberta agrees with embalagem, which is a feminine singular noun.

• embalagem is feminine
• so the adjective must also be feminine singular
• aberto → masculine singular
• aberta → feminine singular

Compare:

• O pacote está aberto.
• A embalagem está aberta.

The adjective matches the noun it describes, not the noun inside the phrase do bolo.

You usually learn a noun’s gender together with the article:

• a embalagem

That tells you it is feminine.

Also, many nouns ending in -agem are feminine in Portuguese:

• a viagem
• a mensagem
• a paisagem
• a embalagem

So once you see a embalagem, it makes sense that the sentence later uses aberta.

It is historically the past participle of abrir (to open), but in this sentence it is functioning as an adjective.

So está aberta means is open, not has opened.

This is very common in Portuguese:

• A porta está fechada. = The door is closed.
• A janela está aberta. = The window is open.

So even though the form comes from a verb, here it describes a state.

In Portuguese, adjectives often come after the noun.

So:

• a embalagem aberta = the open package / packaging

That is the normal order.

In your sentence, the adjective appears after está because it is part of the predicate:

• A embalagem do bolo está aberta.

Very literally:

• The packaging of the cake is open.

English and Portuguese often place adjectives differently, so this is something learners get used to over time.

Usually, no—not if you mean the packaging of the cake.

do bolo means of the cake / the cake’s and refers to a specific cake.

de bolo would sound more like:

• cake packaging
• packaging related to cake in general
• packaging for cake as a type of product

So for this sentence, do bolo is the natural choice.

It can mean packaging, wrapper, or package, depending on context.

In this sentence, embalagem suggests the material or container around the cake—the wrapping, box, or packaging it came in.

A few related words:

• embalagem = packaging / wrapping / package
• pacote = package, packet, parcel
• caixa = box

So A embalagem do bolo está aberta sounds like the cake’s packaging has been opened.

Yes, absolutely. It sounds natural.

A Brazilian might also say similar versions depending on the exact situation:

• O pacote do bolo está aberto.
• A caixa do bolo está aberta.
• O bolo está aberto would usually sound odd, because it is normally the packaging, not the cake itself, that is open.

So your original sentence is perfectly normal when talking about the wrapper, box, or container around the cake.

In Brazilian Portuguese, está is usually pronounced roughly like es-TAH, with the stress on the second syllable.

A very rough guide for the whole sentence is:

A em-ba-LA-gem do BO-lo es-TA a-BER-ta.

A few notes:

• está has a clear stress on -tá
• aberta has stress on ber
• embalagem has stress on the last syllable: -gem

As always, English-style spelling guides are only approximate, but this can help you get started.