The principle parts of the verb eat are:
eat infinitive and present
ate past
eaten past participle
eating present participle
Accordingly, perfect constructions are formed with have + eaten:
I have eaten, you had eaten, he will have eaten, &c
Passive constructions are formed with be + eaten:
We are eaten, you were eaten, they will be eaten, &c
Progressive (continuous) constructions are formed with be + eating:
I am eating, you were eating, she will be eating, &c
You will occasionally hear et for the past, and even for the past participle but in US speech these are strictly non-standard dialect forms.