jmc

We can consider the contributions of the sides of the three layers and the tops of the layers separately. Layer $n$ (counting from the top starting at $1$) has $4$ side faces each with $n$ unit squares, so the sides of the pyramid contribute $4+8+12=24$ for the surface area. The tops of the layers when combined form the same arrangement of unit cubes as the bottom of the pyramid, which is a $3\times 3$ square, hence this contributes $9$ for the surface area. You do not have to count the side underneath, since it is not exposed. Thus, the artist paints $24+9=33\to \boxed{33}$ square meters.