Is it okay to change the research area of interest that I specified in my statement of intent after submitting an application for a PhD program?
Under the conditions you state it is perfectly ok for you to change areas. I doubt that it is even necessary to state it prior to a decision being made on your application, since they don't assign supervisors early on. It might be different if you needed to pick a supervisor prior to acceptance. 

In fact, you would be wise to look carefully at potential supervisors now and after you arrive to be sure you have someone compatible who does work you are interested in. 

However, just as an option, you might want to correspond with the professor mentioning your "broadened" interests and asking for advice. I wouldn't claim you have made a firm decision, but are just exploring your opportunities and would like advice. However, I don't guarantee this is the right approach since I don't know either of you or your past correspondence. You have to judge it.