The total surface area of a triangular square pyramid is calculated by finding the area of the three triangular faces and the square base and adding them together. In this case, the triangular faces have a combined area of 216 (12*18/2) and the square base has an area of 144 (12*12). Adding these together gives a total surface area of 360. To account for the four additional triangular faces on the sides of the pyramid, their combined area would be 216, bringing the total surface area to 576.
