Question
What is the formula for calculating the surface area of a rectangular prism?
Ask by Johnston Higgins. in Nigeria
Jan 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The surface area of a rectangular prism is calculated by adding the areas of all six faces. The formula is:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
Where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Solution
The surface area of a rectangular prism (also known as a cuboid) can be calculated using the formula:
\[
\text{Surface Area} = 2lw + 2lh + 2wh
\]
**Where:**
- \( l \) = length
- \( w \) = width
- \( h \) = height
**Simplified Formula:**
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
**Explanation:**
A rectangular prism has six faces:
- **Top and Bottom:** Each with an area of \( lw \)
- **Front and Back:** Each with an area of \( lh \)
- **Left and Right Sides:** Each with an area of \( wh \)
By calculating the area of each pair of identical faces and summing them up, you obtain the total surface area.
**Example:**
Suppose you have a rectangular prism with:
- Length (\( l \)) = 5 units
- Width (\( w \)) = 3 units
- Height (\( h \)) = 2 units
Plugging these values into the formula:
\[
\text{Surface Area} = 2(5 \times 3) + 2(5 \times 2) + 2(3 \times 2) = 2(15) + 2(10) + 2(6) = 30 + 20 + 12 = 62 \text{ square units}
\]
So, the surface area of the rectangular prism is **62 square units**.
**Summary:**
To find the surface area of a rectangular prism, multiply each pair of dimensions, sum those products, and then multiply by two:
\[
\text{Surface Area} = 2(lw + lh + wh)
\]
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Simplify this solution Beyond the Answer
To calculate the surface area of a rectangular prism, you can use the formula: SA = 2(lw + lh + wh), where 'l' represents the length, 'w' the width, and 'h' the height. Just plug in the measurements of your prism, and voilà! You've got the total surface area to play with. If you're ever into crafting or packaging, this formula comes in handy! Imagine designing a box for gifts or storing snacks—the surface area calculation will help ensure your packages look great and fit everything snugly. Plus, your friends might think you’re a math wizard!
