Area and Perimeter of Polygons

A student comes to class excited. She tells you she has figured out a theory you never told the class. She says she has discovered that as the perimeter of a closed figure increases, the area also increases. She shows you two pictures to prove what she is doing. The first picture is of a 4 by 4 square. Of course, its perimeter is 16 and its area is 16. The second picture is of a 4 by 8 rectangle. Here the perimeter is 24 and the area is 32. What do you say to the student