Finding the surface area of a right rectangular prism (also commonly known as a rectangular box) is a straightforward task once you know the dimensions of the prism. The surface area is the total area of all the exterior surfaces of the prism.
The formula to calculate 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
To apply this formula, follow these steps:
- Measure the dimensions: Start by measuring the length, width, and height of your prism. Make sure to use the same units of measurement for all dimensions (e.g., meters, centimeters, etc.).
- Plug the values into the formula: Insert the measured values into the surface area formula. For instance, if the length is 5 cm, width is 3 cm, and height is 4 cm:
- Perform the calculations: Multiply the dimensions as shown, and then add the results together:
- Final surface area: The surface area of the right rectangular prism with those dimensions is 94 square centimeters (cm²).
SA = 2(5 * 3 + 5 * 4 + 3 * 4)
SA = 2(15 + 20 + 12) = 2(47) = 94 cm²
And that’s it! You’ve successfully calculated the surface area of a right rectangular prism. By understanding this formula and how to apply it, you’ll be able to find the surface area for any right rectangular prism you come across.