To find the total surface area of a rectangular prism (box), we use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given the dimensions:
- Length \( l = 10.5 \) in
- Width \( w = 7 \) in
- Height \( h = 9.1 \) in
Now, we can plug in these values into the surface area formula:
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Calculate each of the products:
- \( lw = 10.5 \times 7 = 73.5 \)
- \( lh = 10.5 \times 9.1 = 95.55 \)
- \( wh = 7 \times 9.1 = 63.7 \)
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Now, sum these values: \[ lw + lh + wh = 73.5 + 95.55 + 63.7 = 232.75 \]
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Finally, multiply by 2 to get the total surface area: \[ \text{Surface Area} = 2 \times 232.75 = 465.5 \]
Therefore, the total surface area of the box is \( \boxed{465.5} \) square inches.