Question

What is the surface area of a rectangular prism whose dimensions are 3 3/4 dm × 4 1/2 dm × 5 dm in square decimeters?(1 point)

Responses
116 1/4 dm^2
84 3/8 dm^2
16 dm^2
58 1/8 dm^2

Answer 1

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

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

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

Given the dimensions:
- \( l = 3 \frac{3}{4} \) dm = \( 3.75 \) dm
- \( w = 4 \frac{1}{2} \) dm = \( 4.5 \) dm
- \( h = 5 \) dm

Now, calculate the products \( lw \), \( lh \), and \( wh \):

1. Calculate \( lw \):
\[
lw = 3.75 \times 4.5 = 16.875 \text{ dm}^2
\]

2. Calculate \( lh \):
\[
lh = 3.75 \times 5 = 18.75 \text{ dm}^2
\]

3. Calculate \( wh \):
\[
wh = 4.5 \times 5 = 22.5 \text{ dm}^2
\]

Now sum these products:
\[
lw + lh + wh = 16.875 + 18.75 + 22.5 = 58.125 \text{ dm}^2
\]

Finally, calculate the surface area:
\[
\text{Surface Area} = 2 \times 58.125 = 116.25 \text{ dm}^2
\]

Convert \( 116.25 \) to a mixed number:
\[
116.25 = 116 \frac{1}{4} \text{ dm}^2
\]

Thus, the surface area of the rectangular prism is:
\[
\boxed{116 \frac{1}{4} \text{ dm}^2}
\]