To find the surface area of a square pyramid, we can use the formula for the surface area \( S \):
\[ S = B + \frac{1}{2} \cdot P \cdot l \]
where:
- \( B \) is the area of the base,
- \( P \) is the perimeter of the base, and
- \( l \) is the slant height.
Step 1: Calculate the area of the base \( B \)
The base of the square pyramid is a square with a width of 15 ft.
\[ B = \text{width}^2 = 15^2 = 225 \text{ ft}^2 \]
Step 2: Calculate the perimeter of the base \( P \)
The perimeter of the square base is given by:
\[ P = 4 \cdot \text{width} = 4 \cdot 15 = 60 \text{ ft} \]
Step 3: Use the slant height \( l \)
The slant height is given as 9.9 ft.
Step 4: Calculate the surface area \( S \)
Now we can substitute \( B \), \( P \), and \( l \) into the surface area formula:
\[ S = B + \frac{1}{2} \cdot P \cdot l \] \[ S = 225 + \frac{1}{2} \cdot 60 \cdot 9.9 \] \[ S = 225 + 30 \cdot 9.9 \] \[ S = 225 + 297 \] \[ S = 522 \text{ ft}^2 \]
Thus, the surface area of the square pyramid is \( 522 \text{ ft}^2 \).
Final Answer:
522 ft.²