To find the surface area of a square pyramid, we can use the formula:
\[ \text{Surface Area} = B + \frac{1}{2} \cdot P \cdot l \]
where:
- \( B \) is the area of the base,
- \( P \) is the perimeter of the base, and
- \( l \) is the slant height of the pyramid.
Given:
- The base of the square pyramid (side length) = 15 ft
- The horizontal length of the triangle (which is commonly interpreted as the slant height) = 9.9 ft
Step 1: Calculate Area of Base \( B \)
Since the base is a square: \[ B = \text{side}^2 = 15 \times 15 = 225 , \text{ft}^2 \]
Step 2: Calculate Perimeter \( P \)
The perimeter of the base (square) is: \[ P = 4 \times \text{side} = 4 \times 15 = 60 , \text{ft} \]
Step 3: Calculate Surface Area
Now, substitute the values into the surface area formula: \[ \text{Surface Area} = B + \frac{1}{2} \cdot P \cdot l \] \[ \text{Surface Area} = 225 + \frac{1}{2} \cdot 60 \cdot 9.9 \] \[ \text{Surface Area} = 225 + 30 \cdot 9.9 \] \[ \text{Surface Area} = 225 + 297 = 522 , \text{ft}^2 \]
Conclusion
The surface area of the square pyramid is 522 ft². Therefore, the correct response is:
522 ft.² (or 522 ft squared)