Question

Find the surface area of a textbook that is 2 in. × 14 in. × 9 in.
1. 172 in.2
2. 50 in.2
3. 344 in.2
4. 252 in.2

Answer 1

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:

1. \( lw = 2 \, \text{in} \times 14 \, \text{in} = 28 \, \text{in}^2 \)
2. \( lh = 2 \, \text{in} \times 9 \, \text{in} = 18 \, \text{in}^2 \)
3. \( wh = 14 \, \text{in} \times 9 \, \text{in} = 126 \, \text{in}^2 \)

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 \( \boxed{344 \, \text{in}^2} \).