I should have included screen shots of the contour lines. Most are closed but a few are open. I should have mentioned that there are two layers, one with the contour lines and another that is a TIN which show the depth inside of the contour lines. Converting the contour areas to polygon removes the depth data.
Maybe my question should be, how can I clip or re-create the TIN so that the TIN only shows the area within the contours. Maybe this is happening because some of the contour lines are not closed? If that is the problem, is it possible to edit the contours to "close" some of the lines?