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 4.5 cm width 3.5 cm and height 2.5 cm
71.5 cm^2
35.75 cm^2
63 cm^2
10.5 cm^2
71.5 cm^2
35.75 cm^2
63 cm^2
10.5 cm^2
Answers
GPT-4o mini
To find the surface area of a right 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:
- Length \( l = 4.5 \) cm
- Width \( w = 3.5 \) cm
- Height \( h = 2.5 \) cm
First, calculate each of the products:
1. \( lw = 4.5 \, \text{cm} \times 3.5 \, \text{cm} = 15.75 \, \text{cm}^2 \)
2. \( lh = 4.5 \, \text{cm} \times 2.5 \, \text{cm} = 11.25 \, \text{cm}^2 \)
3. \( wh = 3.5 \, \text{cm} \times 2.5 \, \text{cm} = 8.75 \, \text{cm}^2 \)
Now add these values together:
\[
lw + lh + wh = 15.75 \, \text{cm}^2 + 11.25 \, \text{cm}^2 + 8.75 \, \text{cm}^2 = 35.75 \, \text{cm}^2
\]
Now, multiply by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 35.75 \, \text{cm}^2 = 71.5 \, \text{cm}^2
\]
Therefore, the surface area of the right rectangular prism is **71.5 cm²**.
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- Length \( l = 4.5 \) cm
- Width \( w = 3.5 \) cm
- Height \( h = 2.5 \) cm
First, calculate each of the products:
1. \( lw = 4.5 \, \text{cm} \times 3.5 \, \text{cm} = 15.75 \, \text{cm}^2 \)
2. \( lh = 4.5 \, \text{cm} \times 2.5 \, \text{cm} = 11.25 \, \text{cm}^2 \)
3. \( wh = 3.5 \, \text{cm} \times 2.5 \, \text{cm} = 8.75 \, \text{cm}^2 \)
Now add these values together:
\[
lw + lh + wh = 15.75 \, \text{cm}^2 + 11.25 \, \text{cm}^2 + 8.75 \, \text{cm}^2 = 35.75 \, \text{cm}^2
\]
Now, multiply by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 35.75 \, \text{cm}^2 = 71.5 \, \text{cm}^2
\]
Therefore, the surface area of the right rectangular prism is **71.5 cm²**.
you sure?
GPT-4o mini
Yes, I can confirm the calculation step by step to ensure accuracy:
1. **Given dimensions:**
- Length \( l = 4.5 \) cm
- Width \( w = 3.5 \) cm
- Height \( h = 2.5 \) cm
2. **Calculate the products:**
- \( lw = 4.5 \times 3.5 = 15.75 \, \text{cm}^2 \)
- \( lh = 4.5 \times 2.5 = 11.25 \, \text{cm}^2 \)
- \( wh = 3.5 \times 2.5 = 8.75 \, \text{cm}^2 \)
3. **Sum the areas of the three pairs of faces:**
\[
lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 \, \text{cm}^2
\]
4. **Multiply by 2 to find the total surface area:**
\[
\text{Surface Area} = 2 \times (lw + lh + wh) = 2 \times 35.75 \, \text{cm}^2 = 71.5 \, \text{cm}^2
\]
Thus, the surface area of the right rectangular prism is indeed **71.5 cm²**. Thank you for double-checking, and if you have further questions, feel free to ask!
1. **Given dimensions:**
- Length \( l = 4.5 \) cm
- Width \( w = 3.5 \) cm
- Height \( h = 2.5 \) cm
2. **Calculate the products:**
- \( lw = 4.5 \times 3.5 = 15.75 \, \text{cm}^2 \)
- \( lh = 4.5 \times 2.5 = 11.25 \, \text{cm}^2 \)
- \( wh = 3.5 \times 2.5 = 8.75 \, \text{cm}^2 \)
3. **Sum the areas of the three pairs of faces:**
\[
lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 \, \text{cm}^2
\]
4. **Multiply by 2 to find the total surface area:**
\[
\text{Surface Area} = 2 \times (lw + lh + wh) = 2 \times 35.75 \, \text{cm}^2 = 71.5 \, \text{cm}^2
\]
Thus, the surface area of the right rectangular prism is indeed **71.5 cm²**. Thank you for double-checking, and if you have further questions, feel free to ask!