Final answer:
surface area of the square based pyramid is 1116.0 ft².
Step-by-step explanation:
To find the surface area of a square based pyramid with a slant height of 22 ft and a side length of 18 ft, we need to calculate both the area of the base and the area of the four triangular faces.
Firstly, the base is a square, so its area is simply the side length squared:
Base area = side length × side length = 18 ft × 18 ft = 324 ft2
Next, the area of one triangular side (since a pyramid has four triangular sides) is found using the formula:
Triangular side area = 1/2 × base × slant height
Since the base of the triangle is the same as the side of the square:
Triangular side area = 1/2 × 18 ft × 22 ft = 9 ft × 22 ft = 198 ft2
Therefore, the total area of the four triangular sides is:
Total triangular area = 4 × triangular side area = 4 × 198 ft2 = 792 ft2
Now, we can add the base area and the total triangular area to find the total surface area:
Total surface area = base area + total triangular area = 324 ft2 + 792 ft2 = 1116 ft2
Finally, round this answer to the tenths place:
Total surface area = 1116.0 ft2