Question

Solve for the surface area of the square pyramid.

(1 point)
Responses

522 ft.2
522 ft. squared

299.25 ft.2
299.25 ft. squared

819 ft.2
819 ft. squared

148.5 ft.2

The square pyramid has 15 ft. of width while the slant height on the right side of it is 9.9 ft.

Answer 1

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