To calculate the total surface area of a rectangular prism, multiply the length (l) by the width (w), the length (l) by the height (h), and the width (w) by the height (h). Multiply each result by 2 and then add them together to get the total surface area.
The Total Surface Area of a Rectangular Prism Calculator is a useful tool to calculate the surface area of any rectangular prism, a 3-dimensional shape with six rectangular faces. This calculator allows you to determine how much surface material is required to cover the prism, making it practical for real-life applications like wrapping or coating objects.
Formula:
SA = 2lw + 2lh + 2wh
| Symbol | Meaning |
|---|---|
| SA | Surface Area |
| l | Length of the Rectangular Prism |
| w | Width of the Rectangular Prism |
| h | Height of the Rectangular Prism |
Solved Calculation:
Example 1:
| Calculation | Instructions |
|---|---|
| Given: l = 10 cm, w = 5 cm, h = 4 cm | Start with the given length, width, and height of the rectangular prism. |
| SA = 2(10 × 5) + 2(10 × 4) + 2(5 × 4) | Multiply the length by the width, the length by the height, and the width by the height. |
| SA = 2(50) + 2(40) + 2(20) | Perform the multiplications. |
| SA = 100 + 80 + 40 | Add the results together. |
| SA = 220 square centimeters | The total surface area is 220 square centimeters. |
Answer: The calculated total surface area is 220 square centimeters.
Example 2:
| Calculation | Instructions |
|---|---|
| Given: l = 6 meters, w = 3 meters, h = 2 meters | Start with the given length, width, and height of the rectangular prism. |
| SA = 2(6 × 3) + 2(6 × 2) + 2(3 × 2) | Multiply the length by the width, the length by the height, and the width by the height. |
| SA = 2(18) + 2(12) + 2(6) | Perform the multiplications. |
| SA = 36 + 24 + 12 | Add the results together. |
| SA = 72 square meters | The total surface area is 72 square meters. |
Answer: The calculated total surface area is 72 square meters.
What is Total Surface Area of a Rectangular Prism ?
To determine the total surface area of a rectangular prism, start by measuring its dimensions: length, width, and height. The total surface area is the sum of the areas of all six faces. Each pair of opposite faces contributes equally, so you’ll account for each dimension in your calculations.
For example, if you have a rectangular prism with specific measurements, you would first calculate the area of each pair of faces. After adding these areas together, you’ll have the total surface area. This measurement is essential for tasks such as painting the surface or calculating materials needed for construction.
If you’re looking for a quick solution, using a total surface area calculator for rectangular prisms can make the process much easier. These online tools allow you to input your dimensions and receive instant results, saving time and ensuring accuracy.
Understanding how to find the total surface area is crucial for various applications, whether it’s for a school project or a practical construction scenario. This knowledge can help in many areas, including design, packaging, and renovation projects.
