Surface Area of Right Rectangular Prisms Quick Check

Question

3 of 53 of 5 Items
Question
Find the surface area of a textbook that is 2 in. × 14 in. × 9 in.
(1 point)
Responses

252 in.2
252 in. squared

172 in.2
172 in. squared

50 in.2
50 in. squared

344 in.2

Answer 1

To find the surface area of a rectangular prism, use the formula:

\[ \text{Surface Area} = 2(lw + lh + wh) \]

where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

For the textbook dimensions given:

• Length (\( l \)) = 2 in.
• Width (\( w \)) = 14 in.
• Height (\( h \)) = 9 in.

Now, plug the values into the formula:

\[ \text{Surface Area} = 2(2 \cdot 14 + 2 \cdot 9 + 14 \cdot 9) \]

Calculate each term inside the parentheses:

1. \( 2 \cdot 14 = 28 \)
2. \( 2 \cdot 9 = 18 \)
3. \( 14 \cdot 9 = 126 \)

Now sum those values: \[ 28 + 18 + 126 = 172 \]

Now, multiply by 2: \[ \text{Surface Area} = 2 \cdot 172 = 344 \]

Thus, the surface area of the textbook is:

\[ \text{Surface Area} = 344 , \text{in}^2 \]

So the correct answer is:

344 in.²