Sox, for a job that size I'd probably use an herbacide. Make sure it's a calm day so the wind doesn't blow the spray on plants you don't want to kill. And if there are other plants close, you can use a drop cloth to protect them until the spray dries.

I can't recommend one spray over another, as I rarely use any. Last year, I grabbed some at the dollar store (of allplaces. Who knows what's really in that stuff?) It was called Maxide and it worked like nothing I've ever seen.

I've tried Roundup, and it was not strong enough to kill our poison ivy and elephant ears. Maxide did it in one spray.

There are probably a few that would work for you.