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

50 in.2
50 in. squared

172 in.2
172 in. squared

344 in.2

Answer 1

To find the surface area of a right rectangular prism (in this case, the textbook), you can use the formula for the surface area \( SA \) given by:

\[ SA = 2(lw + lh + wh) \]

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

For the textbook measurements:

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

Now, substituting those values into the formula:

\[ SA = 2(2 \cdot 14 + 2 \cdot 9 + 14 \cdot 9) \]

Calculating each term:

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

Now, sum these values:

\[ 28 + 18 + 126 = 172 \]

Now multiply by 2:

\[ SA = 2 \cdot 172 = 344 \]

Therefore, the surface area of the textbook is:

\[ \boxed{344 \text{ in}^2} \]