The correct answer is the cardinal is a red bird.
"are" is used for plural nouns (more than one thing). For example "Those people are young" There is more than one person in that sentence, so are is used. Since there is only one cardinal in the given sentence, the answer is not are.
"am" is only used when talking about yourself. For example, "I am a student" is correct since I am talking about myself. "The cardinal am a red bird" is not correct because the cardinal is not talking about itself.
"is" is used with singular nouns (only one thing). Since there is only one cardinal in the sentence, the correct answer is "The cardinal is a red bird". If you need help remembering this, if it is Singular, there will be an s at the end of the verb. For example, "He wants...Cardinal is... She has."
I hope this helps you figure it out in the future =)