Question
12 in. long x 8 in. wide 3 in. tall. what is the surface area
Answers
GPT-4o mini
To calculate the surface area of a rectangular prism (also known as a rectangular box), you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- \( l = 12 \) inches
- \( w = 8 \) inches
- \( h = 3 \) inches
Now, substituting the values into the formula:
1. Calculate \( lw \):
\[
lw = 12 \times 8 = 96 \, \text{in}^2
\]
2. Calculate \( lh \):
\[
lh = 12 \times 3 = 36 \, \text{in}^2
\]
3. Calculate \( wh \):
\[
wh = 8 \times 3 = 24 \, \text{in}^2
\]
Now add these products together:
\[
lw + lh + wh = 96 + 36 + 24 = 156 \, \text{in}^2
\]
Finally, multiply the sum by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 156 = 312 \, \text{in}^2
\]
Therefore, the surface area of the rectangular prism is **312 square inches**.
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- \( l = 12 \) inches
- \( w = 8 \) inches
- \( h = 3 \) inches
Now, substituting the values into the formula:
1. Calculate \( lw \):
\[
lw = 12 \times 8 = 96 \, \text{in}^2
\]
2. Calculate \( lh \):
\[
lh = 12 \times 3 = 36 \, \text{in}^2
\]
3. Calculate \( wh \):
\[
wh = 8 \times 3 = 24 \, \text{in}^2
\]
Now add these products together:
\[
lw + lh + wh = 96 + 36 + 24 = 156 \, \text{in}^2
\]
Finally, multiply the sum by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 156 = 312 \, \text{in}^2
\]
Therefore, the surface area of the rectangular prism is **312 square inches**.