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# Surface area of a cuboid
- URL: https://www.esheets.io/surface-area-of-a-cuboid/
- Published: 2026-01-07T18:28:47.000Z
- Updated: 2026-06-21T16:47:17.000Z
- Author: Richard Linnington
- Tags: Maths, Geometry and Shape

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](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise surface area of a cuboid with this self-marking maths worksheet.

The interactive worksheet below generates questions, gives instant feedback, and lets students record their score.

#### What you’ll practise

- Finding the areas of rectangular faces.
- Recognising the three pairs of equal faces.
- Adding all six face areas.
- Giving the total surface area in square units.

Use the interactive worksheet below, or read the [Topic guide](#topic-guide) for the method and worked example.

## 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.