Question

What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.? (1 point)

O 320 ft.2

Ο 512 ft.2

O 256 ft.2

128 ft.2

Answer 1

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

1. **Area of the base**: The base is a square. The area \( A_{\text{base}} \) of the square base can be calculated using the formula:
\[
A_{\text{base}} = \text{edge}^2 = 8 \, \text{ft} \times 8 \, \text{ft} = 64 \, \text{ft}^2
\]

2. **Area of the triangular faces**: There are four triangular faces, and the area \( A_{\text{triangle}} \) of one triangle can be calculated using the formula:
\[
A_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base of each triangle is the edge of the base (8 ft), and the height is the slant height (16 ft):
\[
A_{\text{triangle}} = \frac{1}{2} \times 8 \, \text{ft} \times 16 \, \text{ft} = \frac{1}{2} \times 128 \, \text{ft}^2 = 64 \, \text{ft}^2
\]
Since there are four triangular faces, the total area for the triangular faces \( A_{\text{triangles}} \) is:
\[
A_{\text{triangles}} = 4 \times A_{\text{triangle}} = 4 \times 64 \, \text{ft}^2 = 256 \, \text{ft}^2
\]

3. **Total surface area**: Now, add the area of the base and the area of the triangular faces together:
\[
\text{Total Surface Area} = A_{\text{base}} + A_{\text{triangles}} = 64 \, \text{ft}^2 + 256 \, \text{ft}^2 = 320 \, \text{ft}^2
\]

Therefore, the surface area of the square pyramid is **320 ft²**.

The correct answer is:
**O 320 ft²**.