Final answer:
To find the surface area of a pyramid, calculate the area of the base and the area of the triangular faces. For this pyramid, the surface area is 338.12 ft².
Step-by-step explanation:
To find the surface area of a pyramid, you need to find the area of the base and the area of the triangular faces.
In this case, the base of the pyramid is a square with side length 18 ft, so the area of the base is 18 ft * 18 ft = 324 ft².
The height of the triangular faces can be found using the Pythagorean Theorem. One leg is the 11 ft height of the pyramid, and the other leg is half of the length of one side of the square base, which is 9 ft (18 ft / 2). Using the theorem, the height of the triangular faces is sqrt(11 ft² - 9 ft²) = sqrt(2 ft²) = 1.41 ft.
The area of each triangular face is (1/2) * 5 ft * 1.41 ft = 3.53 ft².
Since there are 4 triangular faces, the total area of the triangular faces is 4 * 3.53 ft² = 14.12 ft².
Finally, add the area of the base and the area of the triangular faces to find the surface area of the pyramid: 324 ft² + 14.12 ft² = 338.12 ft².