Question

What is the surface area of a square pyramid if the base edge = 68 in. and the slant height = 125 in.?(1 point)
Responses

32,625 in2
32,625 in2
- no response given

17,068 in2
17,068 in2
- incorrect

21,624 in2
21,624 in2
- no response given

17,000 in2

Answer 1

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

1. **Calculate the area of the base**:
\[
\text{Area of the base} = \text{side}^2 = (68 \text{ in})^2 = 4624 \text{ in}^2
\]

2. **Calculate the area of the four triangular faces**:
Each triangular face has a base of 68 in. and a height equal to the slant height of 125 in.
\[
\text{Area of one triangular face} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 68 \text{ in} \times 125 \text{ in} = 4250 \text{ in}^2
\]
Since there are four triangular faces, the total area of the triangular faces is:
\[
\text{Area of four triangular faces} = 4 \times 4250 \text{ in}^2 = 17000 \text{ in}^2
\]

3. **Calculate the total surface area**:
\[
\text{Total Surface Area} = \text{Area of the base} + \text{Area of the triangular faces} = 4624 \text{ in}^2 + 17000 \text{ in}^2 = 21624 \text{ in}^2
\]

Thus, the surface area of the square pyramid is **21,624 in²**.