To find the surface area of a rectangular textbook with dimensions 2 in. × 14 in. × 9 in., you can use the formula for the surface area \( S \) of a rectangular prism:
\[ S = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
In this case, let:
- \( l = 14 , \text{in} \) (length)
- \( w = 2 , \text{in} \) (width)
- \( h = 9 , \text{in} \) (height)
Now, plug these values into the formula:
\[ S = 2(14 \times 2 + 14 \times 9 + 2 \times 9) \]
Calculate each term:
- \( 14 \times 2 = 28 \)
- \( 14 \times 9 = 126 \)
- \( 2 \times 9 = 18 \)
Now sum these products:
\[ 28 + 126 + 18 = 172 \]
Now, substitute back into the surface area formula:
\[ S = 2(172) = 344 , \text{in}^2 \]
Thus, the surface area of the textbook is 344 in.².
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