The surface area of the square pyramid is 45 square meters.
To find the surface area of a square pyramid, we need to calculate the area of the base and the four triangular faces.
Given a square pyramid with a side length of 3 meters and a slant height of 6 meters:
Calculate the base area (square):
Side length = 3 m
Base area = side length² = 3² = 9 m²
Calculate the area of one triangular face:
Base of the triangle (same as the side length of the square base) = 3 m
Slant height = 6 m
Area of one triangular face = 0.5 * base * height = 0.5 * 3 * 6 = 9 m²
Since there are four triangular faces, we multiply the area of one face by 4:
Total area of all triangular faces = 4 * 9 = 36 m²
Add the base area and the total area of the triangular faces to get the surface area of the square pyramid:
Surface area = Base area + Total area of triangular faces = 9 + 36 = 45 m²