Read the sentence.

Brendan is playing in the backyard.

This is an example of a

simple sentence.

compound sentence.

complex sentence.

compound-complex sentence.

This is an example of a simple sentence.

The answer to your question would be that the sentence in question is a simple sentence. A simple sentence in grammar is understood as a sentence with only one main or independent clause and no dependent or subordinate clauses.

By comprising a subject and a predicate, this short syntactic entity intends to convey a complete idea or meanings of idea. In this case, the NP "Brendan" is the subject of the sentence and the VP "is playing in the backyard" is the predicate.