Learn Portuguese (Portugal): O gato está assustado com o barulho.

We use está (from the verb estar) because being frightened is a temporary feeling or state, not a permanent characteristic of the cat. If you used é (from the verb ser), it would mean the cat is by nature a fearful or timid animal.

Why do we use com here when the English translation says "by"?

In English, we usually say someone is "frightened by" or "scared of" something. In Portuguese, the adjective assustado is usually paired with the preposition com (which literally means "with"). You can think of it as the cat being "frightened with" the noise.

If the cat were female, how would this sentence change?

The sentence would become A gata está assustada com o barulho. The adjective assustado changes to its feminine form, assustada, so that it matches the feminine noun a gata.

Can I use the word medo (fear) to say this instead?