A right rectangular prism, also known as a rectangular cuboid, is a three-dimensional shape that has six faces, all of which are rectangles. To calculate the surface area of this prism, you can use a straightforward formula that accounts for all of its rectangular faces.
The formula for the surface area (SA) of a right rectangular prism is:
SA = 2(lw + lh + wh)
Where:
- l = length of the prism
- w = width of the prism
- h = height of the prism
Here’s how to apply the formula:
- First, measure or determine the length, width, and height of the prism.
- Calculate the area of each pair of opposite faces:
- The area of the length and width faces: lw
- The area of the length and height faces: lh
- The area of the width and height faces: wh
- Add these three areas together: lw + lh + wh.
- Multiply the result by 2 to account for both faces of each pair: 2(lw + lh + wh).
For example, if you have a prism with a length of 5 units, a width of 3 units, and a height of 4 units, you would calculate the surface area as follows:
1. Calculate lw = 5 * 3 = 15
2. Calculate lh = 5 * 4 = 20
3. Calculate wh = 3 * 4 = 12
4. Add these areas together: 15 + 20 + 12 = 47
5. And finally, multiply by 2: 2 * 47 = 94
Therefore, the surface area of this specific right rectangular prism would be 94 square units.