Question

Find the surface area for a rectangular prism. This is a composite 3D figure.
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 find the surface area of a rectangular prism, you can use the formula:

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

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

For your rectangular prism:
- Length (\( l \)) = 10 cm
- Width (\( w \)) = 6 cm
- Height (\( h \)) = 12 cm

Now, substitute the values into the formula:

1. Calculate the products inside the parentheses:
- \( lw = 10 \, \text{cm} \times 6 \, \text{cm} = 60 \, \text{cm}^2 \)
- \( lh = 10 \, \text{cm} \times 12 \, \text{cm} = 120 \, \text{cm}^2 \)
- \( wh = 6 \, \text{cm} \times 12 \, \text{cm} = 72 \, \text{cm}^2 \)

2. Add these areas together:
\[
lw + lh + wh = 60 \, \text{cm}^2 + 120 \, \text{cm}^2 + 72 \, \text{cm}^2 = 252 \, \text{cm}^2
\]

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

The surface area of the rectangular prism is \( 504 \, \text{cm}^2 \), not 540 cm as mentioned. Please check the dimensions or if there are any additional areas to consider in the composite figure.