Geometry
Total surface area
The six faces pair into three equal couples, so add the three distinct face areas and double. Measured in square units, not cubic ones.
The Formula
SA = 2(lw + lh + wh)
The six faces pair into three equal couples, so add the three distinct face areas and double. Measured in square units, not cubic ones.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| SA | Total surface area of all six faces | square units | 5200 square centimetres for the 40 x 30 x 20 box. Governs material and wrapping, not capacity. |
| lw + lh + wh | Sum of the three distinct face areas | square units | 1200 + 800 + 600 = 2600 square centimetres before doubling. |
What Each Symbol Means
SAsquare units
Total surface area of all six faces
5200 square centimetres for the 40 x 30 x 20 box. Governs material and wrapping, not capacity.
lw + lh + whsquare units
Sum of the three distinct face areas
1200 + 800 + 600 = 2600 square centimetres before doubling.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the volume of a rectangular prism page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Volume Of A Rectangular Prism, filed under Math. Every number the guide produces comes from substituting into this one line.