Question

Find the surface area of the prism.
7 in.
5 in.
15 in.
Question content area bottom
Part 1
The surface area is
  
enter your response here in.squared.

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, and
- \( h \) is the height.

In your case, you provided the dimensions as \( l = 7 \) in, \( w = 5 \) in, and \( h = 15 \) in.

Let’s substitute these values into the formula:

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

2. Calculate \( lh \):
\[
lh = 7 \, \text{in} \times 15 \, \text{in} = 105 \, \text{in}^2
\]

3. Calculate \( wh \):
\[
wh = 5 \, \text{in} \times 15 \, \text{in} = 75 \, \text{in}^2
\]

4. Now, substitute these into the surface area formula:
\[
\text{Surface Area} = 2(35 + 105 + 75)
\]

5. Calculate the sum inside the parentheses:
\[
35 + 105 + 75 = 215 \, \text{in}^2
\]

6. Finally, multiply by 2:
\[
\text{Surface Area} = 2 \times 215 = 430 \, \text{in}^2
\]

Therefore, the surface area of the prism is \( \boxed{430} \) in².