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.