Question

Which of the following correctly calculates the surface area of a rectangular prism with a length of 6 ft., a width of 14 ft., and a height of 12 ft.?

Answer 1

To calculate the surface area \( S \) of a rectangular prism, you can use the formula:

\[
S = 2(lw + lh + wh)
\]

where:
- \( l \) is the length,
- \( w \) is the width, and
- \( h \) is the height.

Given:
- Length \( l = 6 \) ft,
- Width \( w = 14 \) ft,
- Height \( h = 12 \) ft.

Now, substituting the values into the formula:

1. Calculate \( lw \):
\[
lw = 6 \times 14 = 84 \, \text{sq ft}
\]

2. Calculate \( lh \):
\[
lh = 6 \times 12 = 72 \, \text{sq ft}
\]

3. Calculate \( wh \):
\[
wh = 14 \times 12 = 168 \, \text{sq ft}
\]

4. Now add these areas together:
\[
lw + lh + wh = 84 + 72 + 168 = 324 \, \text{sq ft}
\]

5. Finally, multiply by 2 to get the surface area:
\[
S = 2(324) = 648 \, \text{sq ft}
\]

Therefore, the surface area of the rectangular prism is \( \boxed{648} \) square feet.