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:
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\( 2lw = 2 \times 9 \times 7 \) \[ 2lw = 2 \times 9 \times 7 = 126 \text{ in}^2 \]
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\( 2hw = 2 \times 13 \times 7 \) \[ 2hw = 2 \times 13 \times 7 = 182 \text{ in}^2 \]
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\( 2lh = 2 \times 9 \times 13 \) \[ 2lh = 2 \times 9 \times 13 = 234 \text{ in}^2 \]
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 \( 542 \text{ in}^2 \).