Question
Find the surface area of a rectangular prism prism (a box) if the dimensions are 4 m wide, 6 m long, and 3 m high
Ask by Dickson George. in the United States
Dec 14,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The surface area of the rectangular prism is 108 m².
Solution
To find the surface area of a rectangular prism (or box), you can use the formula:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Width (\( w \)) = 4 m
- Length (\( l \)) = 6 m
- Height (\( h \)) = 3 m
Now, plug in the values:
\[
\text{Surface Area} = 2(6 \times 4 + 6 \times 3 + 4 \times 3)
\]
Calculating each term inside the parentheses:
1. \( 6 \times 4 = 24 \)
2. \( 6 \times 3 = 18 \)
3. \( 4 \times 3 = 12 \)
Now, add these results together:
\[
24 + 18 + 12 = 54
\]
Now, multiply by 2:
\[
\text{Surface Area} = 2 \times 54 = 108 \, \text{m}^2
\]
Thus, the surface area of the rectangular prism is \( \boxed{108} \, \text{m}^2 \).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To find the surface area of a rectangular prism, you can use the formula: Surface Area = 2(lw + lh + wh). Here, l (length) is 6 m, w (width) is 4 m, and h (height) is 3 m. Plugging in the values, we perform the calculations: \(2(6 \times 4 + 6 \times 3 + 4 \times 3) = 2(24 + 18 + 12) = 2(54) = 108 \, m^2\). So, the surface area is 108 square meters! In real life, understanding how to calculate the surface area of a rectangular prism comes in handy more often than you think! If you're wrapping a package, building a box, or even determining how much paint you need for a room with prism-like walls, knowing this formula can save you time and ensure you don’t end up with an unfinished project!
