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To calculate the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base (which is a square) is given by the formula A = s^2, where s is the length of one side of the square. In this case, the base length is 12, so the area of the base is 12^2 = 144 square units.
Next, we need to find the area of one of the triangular faces. The formula for the area of a triangle is A = 0.5 * base * height. Since the base is the same as the side length of the square base (12), we just need to find the height of the triangle, which is the slant height of the pyramid. In this case, the slant height is 18, so the area of one triangular face is 0.5 * 12 * 18 = 108 square units.
Since there are four triangular faces on a square pyramid, the total area of all four faces is 4 * 108 = 432 square units.
Finally, we add the area of the base to the total area of the four triangular faces to find the total surface area of the pyramid:
144 (base) + 432 (triangular faces) = 576 square units.
Therefore, the surface area of the square pyramid is 576 square units.