Hollywood Florida broker fee

I used Zillow to find a seasonal rental(Dec-Feb) in Hollywood Florida. On Zillow, the contact was a broker, and we worked an agreement and just received the contract. The contract has a clause asking us to pay the broker one half of the first months rent as a fee on top of the rent. I had assumed that the renter paid this, because I did not ask the broker to find me an apartment, I found it on Zillow and the broker was the contact. Any advice as to whether this is standard, or should I push back. We never discussed fees with the broker.