Problem 18

Given a pyramid $SACB$ with vertex $S$ whose base is a right triangle $ACB$ in which $[ AB ]$ is a hypotenuse with length $2\sqrt3 \text{ cm}$ . The lateral edge $[ SA ]$ is perpendicular to the plane of the base. The dihedral angle formed by the lateral face $SAC$ and $SAB$ is $30^\circ$ . The altitude of the pyramid is $4\text{ cm}$ in length. Find the lateral area.