A cuboid is a solid figure with six rectangular faces. The most common examples of cuboids include boxes, books, bricks, and even a large number of packages. Calculation of the surface area of a cuboid enables one to determine the whole area occupied by its outer faces.
How to calculate the surface area of a cuboid? You just need the dimensions of the cuboid and use the right formula.
What Is the Surface Area of a Cuboid?
A cuboid surface area is the total surface area of the six rectangular faces of a cuboid. Opposite sides of a cuboid are identical; therefore, we get:
- Top and bottom face: length × width
- Front and back face: length × height
- Left and right face: width × height
Total surface area can be obtained by summing the areas of all the six faces.
What Is a Cuboid?
Parts of a Cuboid
A cuboid is a three-dimensional shape with three main dimensions: length, width, and height. Understanding these dimensions makes it easier to calculate the surface area and volume of a cuboid.
Length, Width & Height
Parts of a Cuboid
Dimensions of a Cuboid
To find the surface area of a cuboid, you need its length, width, and height. These three measurements are usually represented by l, w, and h.
Formula for Surface Area of a Cuboid
Surface Area = 2(lw + lh + wh)
where,
- l = length
- w = width
- h = height
Multiplication with 2 is done because there are two faces of each rectangle.
How to Find the Surface Area of a Cuboid
All you need to do in order to find the surface area of a cuboid is to use the following simple steps:
- Find the length, width, and height of it.
- Use the formula: SA = 2(lw + lh + wh).
- Substitute the values in the formula.
- Find out the value of lw, lh, and wh.
- Add the values obtained in the previous step together.
- Multiply the result by 2.
- Present the result in square units.
- Example of the Calculation of the Surface Area of a Cuboid
Example: Find the Surface Area of a Cuboid
Length = 8 cm
Width = 5 cm
Height = 3 cm
Then we get:
SA = 2(lw + lh + wh)
= 2[(8 × 5) + (8 × 3) + (5 × 3)]
= 2(40 + 24 + 15)
= 158 cm²
Thus, the surface area of a cuboid is 158 cm².
Recommended Reading: What is 9/5 as a decimal?
Total Surface Area vs. Volume
Surface area and volume measure different things.
Measurement | Formula | Unit |
Surface Area | 2(lw + lh + wh) | Square units |
Volume | l × w × h | Cubic units |
Surface area measures the outside of the cuboid, while volume measures the space inside it.
Common Mistakes to Be Avoided
While calculating the surface area of a cuboid, one should:
- Consider all three measurements.
- Multiply the total by 2.
- Maintain uniformity of the unit of measurement.
- Use square units, for example, cm² or m².
- Not get confused with the formulas of the surface area and volume of a cuboid.
Conclusion
Finding the surface area of a cuboid is an easy task as soon as you have its three dimensions. Recall the formula 2 (lw + lh + wh), put the measures into the equation in the right way, and you will get your final answer in square units.
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