Question

Find the surface area of the prism.
Length: 5 in.
Width: 4 in.
Height: 7 in.

Answer 1

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

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

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

Given:
- Length (\( l \)) = 5 in
- Width (\( w \)) = 4 in
- Height (\( h \)) = 7 in

Now plug these values into the formula:

1. Calculate \( lw \):
\[
lw = 5 \times 4 = 20 \, \text{in}^2
\]

2. Calculate \( lh \):
\[
lh = 5 \times 7 = 35 \, \text{in}^2
\]

3. Calculate \( wh \):
\[
wh = 4 \times 7 = 28 \, \text{in}^2
\]

4. Now sum these areas:
\[
lw + lh + wh = 20 + 35 + 28 = 83 \, \text{in}^2
\]

5. Finally, multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 83 = 166 \, \text{in}^2
\]

Thus, the surface area of the prism is \( \boxed{166} \) square inches.