Question

Find the surface area of a square pyramid with side length 2 ft and slant height 3 ft.
2 ft
2 ft
3 ft
Answer
Attempt 1 out of 2

Answer 1

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

1. **Calculate the area of the base:**
The base of the pyramid is a square with side length \( s = 2 \) ft.

\[
\text{Area of the base} = s^2 = 2^2 = 4 \text{ ft}^2
\]

2. **Calculate the area of the triangular faces:**
Each triangular face has a base of the same length as the side of the square base and a height equal to the slant height of the pyramid.

The area of one triangular face can be calculated as:

\[
\text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 3 = 3 \text{ ft}^2
\]

Since there are 4 triangular faces, the total area of the triangular faces is:

\[
\text{Total area of triangular faces} = 4 \times 3 = 12 \text{ ft}^2
\]

3. **Calculate the total surface area:**
Finally, we add the area of the base to the total area of the triangular faces:

\[
\text{Total surface area} = \text{Area of the base} + \text{Total area of triangular faces} = 4 + 12 = 16 \text{ ft}^2
\]

Therefore, the surface area of the square pyramid is \( \boxed{16} \) ft².