Question
Use the formula for the surface area of a right rectangular prism to find the surface area of a shape with the following measurements length =4.5cm , width =3.5cm , and heigh t =2.5cm (1 point) 71.5cm^2 35.75cm^2 63cm^2 10.5cm^2
Answers
GPT-4o mini
The formula for the surface area \( SA \) of a right rectangular prism is given by:
\[
SA = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length \( l = 4.5 \) cm,
- Width \( w = 3.5 \) cm,
- Height \( h = 2.5 \) cm.
Let's plug the values into the formula:
1. Calculate \( lw \):
\[
lw = 4.5 \times 3.5 = 15.75 \, \text{cm}^2
\]
2. Calculate \( lh \):
\[
lh = 4.5 \times 2.5 = 11.25 \, \text{cm}^2
\]
3. Calculate \( wh \):
\[
wh = 3.5 \times 2.5 = 8.75 \, \text{cm}^2
\]
Now, add these areas together:
\[
lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 \, \text{cm}^2
\]
Finally, multiply by 2 to find the surface area:
\[
SA = 2 \times 35.75 = 71.5 \, \text{cm}^2
\]
So, the surface area of the right rectangular prism is \( \boxed{71.5 \, \text{cm}^2} \).
\[
SA = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length \( l = 4.5 \) cm,
- Width \( w = 3.5 \) cm,
- Height \( h = 2.5 \) cm.
Let's plug the values into the formula:
1. Calculate \( lw \):
\[
lw = 4.5 \times 3.5 = 15.75 \, \text{cm}^2
\]
2. Calculate \( lh \):
\[
lh = 4.5 \times 2.5 = 11.25 \, \text{cm}^2
\]
3. Calculate \( wh \):
\[
wh = 3.5 \times 2.5 = 8.75 \, \text{cm}^2
\]
Now, add these areas together:
\[
lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 \, \text{cm}^2
\]
Finally, multiply by 2 to find the surface area:
\[
SA = 2 \times 35.75 = 71.5 \, \text{cm}^2
\]
So, the surface area of the right rectangular prism is \( \boxed{71.5 \, \text{cm}^2} \).