Question

Solve for the surface area of the square pyramid.

(1 point)
Responses

522 ft.2
522 ft. squared

148.5 ft.2
148.5 ft. squared

819 ft.2
819 ft. squared

299.25 ft.2

I got 507 but that’s not the right answer

The base of the base square is : 15
The triangle has the number 9.9 horizontally on the triangle.

Answer 1

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**)