Surface area of a cuboid
Calculating surface area is a vital skill for real-world projects, such as determining exactly how much paint is needed to cover a room or how much cardboard is required to manufacture a packaging box. It helps us measure the total area of every outside face on a 3D object. Jump to the questions
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Topic guide
What this worksheet practises
This worksheet focuses on calculating the total surface area of a cuboid (a rectangular box). Unlike a cube, the faces of a cuboid are not all the same size. However, they do come in matching pairs.
Key method
A cuboid has 6 rectangular faces, consisting of 3 matching pairs: Top/Bottom, Front/Back, and Left/Right.
- Identify the three different dimensions of the cuboid: Length, Width, and Height.
- Calculate the area of the Front face (Length × Height) and double it (to include the Back).
- Calculate the area of the Top face (Length × Width) and double it (to include the Bottom).
- Calculate the area of the Side face (Width × Height) and double it (to include the other Side).
- Add these three pairs together to get the total surface area.
Worked example
Calculate the surface area of a cuboid with length 10cm, width 4cm, and height 5cm.
Step 1: Calculate Front/Back pair.
Front = 10 × 5 = 50.
Pair = 50 × 2 = 100.
Step 2: Calculate Top/Bottom pair.
Top = 10 × 4 = 40.
Pair = 40 × 2 = 80.
Step 3: Calculate Side/Side pair.
Side = 4 × 5 = 20.
Pair = 20 × 2 = 40.
Step 4: Add them all together.
100 + 80 + 40 = 220.
The total surface area is 220 cm².
Common mistakes to avoid
The most common mistake is forgetting to double the faces. A student might correctly calculate Front(50) + Top(40) + Side(20) = 110, but then stop. This only gives half the surface area (3 faces). A cuboid has 6 faces, so you must always remember the hidden pairs.
Things to remember
A quick mental check to ensure you haven't missed any combinations: If the dimensions are numbers A, B, and C, your three area calculations should be (A×B), (B×C), and (A×C). Every number must multiply every other number once.