To find the total surface area of a rectangular prism, we use the formula:
\[ SA = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
From the description, we have:
- Length \( l = 7 \) inches
- Width \( w = 9.1 \) inches
- Height \( h = 12.4 \) inches
Now we can compute each of the areas of the three different pairs of faces:
-
The area of the length and width faces: \[ lw = 7 \times 9.1 = 63.7 \quad \text{(square inches)} \]
-
The area of the length and height faces: \[ lh = 7 \times 12.4 = 86.8 \quad \text{(square inches)} \]
-
The area of the width and height faces: \[ wh = 9.1 \times 12.4 = 112.84 \quad \text{(square inches)} \]
Now we plug these values into the surface area formula:
\[ SA = 2(63.7 + 86.8 + 112.84) \]
Calculating the sum inside the parentheses:
\[ 63.7 + 86.8 + 112.84 = 263.34 \]
Now, we multiply this sum by 2 to find the total surface area:
\[ SA = 2 \times 263.34 = 526.68 \]
Thus, the total surface area of the box is:
\[ \boxed{526.68} \quad \text{square inches} \]