1999 Gauss 8 Problem 25

Four identical isosceles triangles border a square of side 6 cm, as shown. When the four triangles are folded up they meet at a point to form a pyramid with a square base. If the height of this pyramid is 4 cm, the total area of the four triangles and the square is

\textbf{(A)}\ 84\,\text{cm}^2\quad \textbf{(B)}\ 98\,\text{cm}^2\quad \textbf{(C)}\ 96\,\text{cm}^2\quad \textbf{(D)}\ 108\,\text{cm}^2\quad \textbf{(E)}\ 90\,\text{cm}^2

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.