To find the total surface area of a rectangular prism (box), 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 of the prism.
In your case, the dimensions of the box are:
- Length (\( l \)) = 12.4 inches
- Width (\( w \)) = 7 inches
- Height (\( h \)) = 9.1 inches
Now, plug these dimensions into the formula:
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Calculate \( lw \): \[ lw = 12.4 \times 7 = 86.8 , \text{square inches} \]
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Calculate \( lh \): \[ lh = 12.4 \times 9.1 = 113.84 , \text{square inches} \]
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Calculate \( wh \): \[ wh = 7 \times 9.1 = 63.7 , \text{square inches} \]
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Now add these areas together: \[ lw + lh + wh = 86.8 + 113.84 + 63.7 = 264.34 , \text{square inches} \]
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Finally, multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times 264.34 = 528.68 , \text{square inches} \]
So, the total surface area of the box is \( \boxed{528.68} \) square inches.