Add Scrollable Textarea(s) To Scrollable DIV?

The scenario is, a scrollable DIV on a webpage. Within the DIV is a scrollable textarea. Beside the DIV is a button whose onclick event creates and places another scrollable textarea below the first. Any subsequent onclick events places another scrollable textarea below the previous. I'm fairly sure that CSS will come into play for positioning of additional textarea's. My thinking is to create an array for the first textarea ID, then increase the array by 1 on any subsequent onclick event, then assign contents (values) of textarea(s) to ID's using innerHTML. Is this approach plausable, or is there a simpler method to this madness? Is there a method/function for calculating the height (px)of a textarea with overflow set to auto, regardless of text length within.