jmc

The triangular faces are isosceles triangles. We drop an altitude from the apex to the base, and, since the triangle is isosceles, it will also be a median. So it forms a right triangle with hypotenuse $5$ and one leg $3$, and thus the other leg, the altitude, is $4$. The area of the triangle is then $\frac{4(6)}{2}=12$. Since there are $4$ triangular faces, the total area is $4(12)=\boxed{48}$.