Question

Filip is making a crate that is a prism with a square base. The base side length is 8 in. and the height of the prism is 20 in. Which of the following correctly calculates the surface area of this prism?

Answer 1

To calculate the surface area of a prism with a square base, you can use the formula:

\[
\text{Surface Area} = 2B + Ph
\]

where:
- \(B\) is the area of the base,
- \(P\) is the perimeter of the base, and
- \(h\) is the height of the prism.

1. **Calculate the base area (B)**:
- The base is square, so the area \(B\) is given by:
\[
B = \text{side}^2 = 8 \, \text{in} \times 8 \, \text{in} = 64 \, \text{in}^2
\]

2. **Calculate the perimeter (P)**:
- The perimeter of a square is given by:
\[
P = 4 \times \text{side} = 4 \times 8 \, \text{in} = 32 \, \text{in}
\]

3. **Use the height (h)**:
- Given height \(h = 20 \, \text{in}\).

4. **Plug these values into the surface area formula**:
\[
\text{Surface Area} = 2B + Ph = 2(64 \, \text{in}^2) + (32 \, \text{in} \times 20 \, \text{in})
\]

- Calculate \(2B\):
\[
2B = 2 \times 64 \, \text{in}^2 = 128 \, \text{in}^2
\]

- Calculate \(Ph\):
\[
Ph = 32 \, \text{in} \times 20 \, \text{in} = 640 \, \text{in}^2
\]

5. **Add the two results to find the total surface area**:
\[
\text{Surface Area} = 128 \, \text{in}^2 + 640 \, \text{in}^2 = 768 \, \text{in}^2
\]

Therefore, the surface area of the prism is \(768 \, \text{in}^2\).