Question

formula for rectangular prism: SA =2lw + 2hw + 2lh
use this formula to find the surface area of a rectangular prism that has :
9 in length, 7 in width, and 13 in height

Answer 1

To find the surface area (SA) of a rectangular prism using the formula \( SA = 2lw + 2hw + 2lh \), we can substitute the given values for length (l), width (w), and height (h).

- Length (\( l \)) = 9 inches
- Width (\( w \)) = 7 inches
- Height (\( h \)) = 13 inches

Now, we can calculate each term in the formula:

1. \( 2lw = 2 \times 9 \times 7 \)
\[
2lw = 2 \times 9 \times 7 = 126 \text{ in}^2
\]

2. \( 2hw = 2 \times 13 \times 7 \)
\[
2hw = 2 \times 13 \times 7 = 182 \text{ in}^2
\]

3. \( 2lh = 2 \times 9 \times 13 \)
\[
2lh = 2 \times 9 \times 13 = 234 \text{ in}^2
\]

Now, we can add all these values together to find the total surface area:

\[
SA = 2lw + 2hw + 2lh = 126 + 182 + 234
\]

Calculating the sum:

\[
SA = 126 + 182 + 234 = 542 \text{ in}^2
\]

Thus, the surface area of the rectangular prism is \( 542 \text{ in}^2 \).