Question

Solve for the surface area of the square pyramid. 15ft and 9.9 ft
148.5ft*2
819 feet *2
299.25 feet *2
522 ft *2

Answer 1

To find the surface area of a square pyramid, you need to consider both the base and the triangular faces.

Given:
- Base side length \( s = 15 \) ft
- Height (slant height) of the triangular face \( l = 9.9 \) ft

### Surface Area Calculation

1. **Area of the Square Base:**
\[
\text{Area of base} = s^2 = 15^2 = 225 \text{ ft}^2
\]

2. **Area of the Triangular Faces:**
A square pyramid has 4 triangular faces, and the area of one triangular face is given by:
\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times s \times l
\]
Substituting the \( s \) and \( l \):
\[
\text{Area of one triangle} = \frac{1}{2} \times 15 \times 9.9 = \frac{1}{2} \times 148.5 = 74.25 \text{ ft}^2
\]

Then, for the four triangular faces:
\[
\text{Total area of four triangles} = 4 \times 74.25 = 297 \text{ ft}^2
\]

3. **Total Surface Area:**
Add the area of the base to the total area of the triangular faces:
\[
\text{Total Surface Area} = \text{Area of base} + \text{Total area of triangles} = 225 + 297 = 522 \text{ ft}^2
\]

### Answer
So, the surface area of the square pyramid is \( \boxed{522 \text{ ft}^2} \).