Question

Find the surface area for a rectangular prism.
Length is 10 cm, width is 6 cm and height is 12 cm
Shows answer as 540 cm.
How do I do this problem

Answer 1

To calculate the surface area of a rectangular prism, you can use the following formula:

\[
\text{Surface Area} = 2(lb + lh + wh)
\]

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

In your case:
- Length (\( l \)) = 10 cm
- Width (\( w \)) = 6 cm
- Height (\( h \)) = 12 cm

Now, plug the values into the formula:

1. Calculate \( lb \) (length × width):
\[
lb = 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2
\]

2. Calculate \( lh \) (length × height):
\[
lh = 10 \, \text{cm} \times 12 \, \text{cm} = 120 \, \text{cm}^2
\]

3. Calculate \( wh \) (width × height):
\[
wh = 6 \, \text{cm} \times 12 \, \text{cm} = 72 \, \text{cm}^2
\]

4. Now sum these areas:
\[
lb + lh + wh = 60 \, \text{cm}^2 + 120 \, \text{cm}^2 + 72 \, \text{cm}^2 = 252 \, \text{cm}^2
\]

5. Finally, multiply the sum by 2 to find the total surface area:
\[
\text{Surface Area} = 2 \times 252 \, \text{cm}^2 = 504 \, \text{cm}^2
\]

So, the surface area of the rectangular prism is \( 504 \, \text{cm}^2 \), not \( 540 \, \text{cm}^2 \). It's possible there was a calculation mistake in arriving at that other number. The correct surface area is \( 504 \, \text{cm}^2 \).