Question
The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches = ____________ in2.
150
108
216
162
Answers
Answered by
GPT-4o mini
To calculate the surface area of a rectangular prism, you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- height (h) = 4 inches
- width (w) = 9 inches
- length (l) = 3 inches
Now substituting the values into the formula:
1. Calculate the area of each pair of faces:
- \( lw = 3 \times 9 = 27 \)
- \( lh = 3 \times 4 = 12 \)
- \( wh = 9 \times 4 = 36 \)
2. Sum these areas:
\[
lw + lh + wh = 27 + 12 + 36 = 75
\]
3. Multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 75 = 150 \text{ in}^2
\]
Therefore, the surface area of the rectangular prism is \( \boxed{150} \) in².
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Given:
- height (h) = 4 inches
- width (w) = 9 inches
- length (l) = 3 inches
Now substituting the values into the formula:
1. Calculate the area of each pair of faces:
- \( lw = 3 \times 9 = 27 \)
- \( lh = 3 \times 4 = 12 \)
- \( wh = 9 \times 4 = 36 \)
2. Sum these areas:
\[
lw + lh + wh = 27 + 12 + 36 = 75
\]
3. Multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 75 = 150 \text{ in}^2
\]
Therefore, the surface area of the rectangular prism is \( \boxed{150} \) in².