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# Compound area
- URL: https://www.esheets.io/compound-area/
- Published: 2024-09-28T17:04:25.000Z
- Updated: 2026-06-21T16:41:52.000Z
- Author: Richard Linnington
- Tags: Maths, Geometry and Shape

Understanding how to calculate the area of compound shapes is important in real-world situations like designing a park, building a garden, or even arranging furniture in a room. By breaking down complex shapes into simpler ones like rectangles, triangles, or circles, you can find the total area with ease—an essential skill in architecture, engineering, and everyday problem-solving. [Jump to the questions](#practise-now)

## Practise now

Worksheet preview and key skills 

### Worksheet preview

Practise compound area 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

- Splitting a compound shape into simpler shapes.
- Finding missing side lengths where needed.
- Adding or subtracting areas carefully.
- Giving the final area in square units.

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

**Round all answers to the nearest whole number.** For relevant questions either use the pi button on your calculator or use 3.142 instead.

  
## Topic guide

### What this worksheet practises

This worksheet focuses on calculating the area of compound shapes. A compound shape (or composite shape) is simply a shape made up of two or more basic geometric figures, such as rectangles and triangles joined together.

### Key method

To find the total area, you must split the complex shape into simpler parts that you already know how to calculate.

- Draw a straight line across the shape to split it into two or more distinct rectangles or triangles.
- Use the given side lengths to deduce any missing side lengths required for your new, smaller shapes.
- Calculate the area of each individual shape separately.
- Add all the individual areas together to find the total compound area.

### Worked example

**Find the area of an L-shape that can be split into a 5cm by 2cm rectangle and a 3cm by 4cm rectangle.**

Step 1: Identify the split. The shape is now Rectangle A and Rectangle B.

Step 2: Calculate the area of Rectangle A.

Area A = 5 × 2 = 10 cm².

Step 3: Calculate the area of Rectangle B.

Area B = 3 × 4 = 12 cm².

Step 4: Add the areas together.

Total Area = 10 + 12 = 22 cm².

### Common mistakes to avoid

A common mistake is multiplying all the exterior lengths together indiscriminately. You must calculate the individual areas first. Another frequent trap is forgetting to deduce missing lengths; you often have to subtract a shorter side from a longer side to find the dimension of one of your split rectangles.

### Things to remember

There is usually more than one correct way to split a compound shape. Whether you split an L-shape vertically or horizontally, the total final area will always be exactly the same.