Surface Area of a Rectangular Prism Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the surface area of a rectangular prism?
Answer
Surface area of a rectangular prism
S = 2 · (a·b + a·h + b·h)
Here a is the side (or base), b is the second side, h is the height, perpendicular to the base. The result comes out in square units.
Where the formula comes from
S = 2 · (a·b + a·h + b·h)
Six faces in three matching pairs: top and bottom are a·b, front and back are a·h, the two sides are b·h. Add one of each and double.
Worked examples
Let a = 5, b = 4, h = 3. Then the surface area of a rectangular prism = 94 square units.
Let a = 2.5, b = 6, h = 1.2. Then the surface area of a rectangular prism = 50.4 square units.
The common mistake
Doubling only the first pair. The 2 multiplies the whole bracket, not just a·b — every one of the three pairs has two members.
Other quantities: Rectangular prism
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See Also
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- Square Meters to Square Feet (Sq M to Sq Ft) - Convert Square Meters to Square Feet
- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the surface area of a rectangular prism? (The answer is: S = 2 · (a·b + a·h + b·h)). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter
Values from the Formula (b = 4, h = 3)
| If a = | Surface area |
|---|---|
| 1 | 38 square units |
| 2 | 52 square units |
| 3 | 66 square units |
| 4 | 80 square units |
| 5 | 94 square units |
| 10 | 164 square units |
FAQ
What is the formula for the surface area of a rectangular prism?
Surface area of a rectangular prism S = 2 · (a·b + a·h + b·h)
Where does this formula come from?
Six faces in three matching pairs: top and bottom are a·b, front and back are a·h, the two sides are b·h. Add one of each and double.
What is the most common mistake here?
Doubling only the first pair. The 2 multiplies the whole bracket, not just a·b — every one of the three pairs has two members.
How do I use this formula?
Put your own numbers in place of the letters. With a = 2.5, b = 6, h = 1.2, for instance, the formula S = 2 · (a·b + a·h + b·h) gives = 50.4 square units.
See Also
- Diameter of a Circle Formula
- Perimeter of a Regular Polygon Formula
- Perimeter of a Rectangle Formula
- Perimeter of a Semicircle Formula
- Perimeter of a Square Formula
- Perimeter of a Triangle Formula
- Surface Area of a Cone Formula
- Surface Area of a Cube Formula
- Surface Area of a Cylinder Formula
- Surface Area of a Pyramid Formula
- Surface Area of a Sphere Formula
- Surface Area of a Triangular Prism Formula
- Volume of a Cone Formula
- Volume of a Cube Formula
- Volume of a Cylinder Formula
- Volume of a Pyramid Formula
- Volume of a Rectangular Prism Formula
- Volume of a Sphere Formula
- Volume of a Triangular Prism Formula
- Площадь поверхности параллелепипеда
- Área de la superficie del prisma rectangular
- Área da superfície do prisma retangular