To find the surface area of a rectangular prism (which a textbook is modeled as), we use the formula for the surface area \( S \):
\[ S = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
In this case, the dimensions of the textbook are:
- Length \( l = 2 , \text{in} \)
- Width \( w = 14 , \text{in} \)
- Height \( h = 9 , \text{in} \)
Now, we will calculate each of the areas of the three different pairs of sides:
- \( lw = 2 , \text{in} \times 14 , \text{in} = 28 , \text{in}^2 \)
- \( lh = 2 , \text{in} \times 9 , \text{in} = 18 , \text{in}^2 \)
- \( wh = 14 , \text{in} \times 9 , \text{in} = 126 , \text{in}^2 \)
Now we will plug these values into the surface area formula:
\[ S = 2(28 + 18 + 126) \]
Calculating the sum inside the parentheses:
\[ 28 + 18 + 126 = 172 \]
Now, multiply by 2:
\[ S = 2 \times 172 = 344 , \text{in}^2 \]
Thus, the surface area of the textbook is \( \boxed{344 , \text{in}^2} \).
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