Curriculum Hub → Maths Lessons → Geometry → Perimeter and Area → Area of Compound Shapes
Ready-to-teach lesson. Includes PowerPoint, printable worksheet and fully worked solutions. Saves 2+ hours of planning.
To find the area of compound shapes, split the shape into simpler shapes such as rectangles, triangles or circles. Calculate the area of each part, then add or subtract them to find the total area.
This is a key topic in GCSE maths. Students need to recognise how shapes can be split, apply the correct formulas, and organise their working clearly.
Watch this tutorial first to see how to split compound shapes and find missing lengths. Then try the free worksheet below.
⏱️ Video length: 5 minutes | Key topics: Splitting shapes, finding missing lengths, addition vs subtraction method
Download the free GCSE worksheet. It includes exam-style compound area questions, space for working, and a full answer key.
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This section provides a walkthrough of the full lesson, including editable PowerPoint slides, differentiated worksheets, and teaching strategies refined over 20 years of classroom practice.
Below, you will find sample materials from the lesson alongside a step-by-step teaching guide covering how to introduce the topic, structure independent practice, and address common misconceptions.
Once students have secured their understanding of compound areas, members can extend learning with a dedicated revision lesson on area of 2D shapes and a separate problem-solving lesson that applies perimeter and area in unfamiliar contexts.
Use this approach for compound rectilinear shapes in GCSE maths (also called composite shapes):
Best for: L-shapes, T-shapes, most GCSE questions.
Best for: shapes with a missing corner or cut-out.
Start with a clear definition. Ask students to discuss in pairs what a compound shape is, then refine it using the figures below: one shape formed from a combination of rectangles.
Display the shapes and ask the class to find different arrangements of rectangles that produce the same pink compound shape.
Next, ask students to calculate the same area using all three approaches and circle the method they find quickest.
Then set independent practice. Students who finish early try a second method to check their answer. Both addition and subtraction are valid when the reasoning is clear.
Allow about twelve minutes. Stress identifying the rectangles and labelling lengths carefully before calculating.
If students are stuck, model how the blue region can be seen as a combination of rectangles:
For more support, break the central part into individual rectangles and record each dimension first:
Try these 4 GCSE-style questions, then reveal the solutions to check your working.
How to use these questions in class
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A compound shape (also called a composite shape) is a single outline made by joining two or more simpler shapes, such as rectangles. In GCSE maths, most compound area questions use rectilinear shapes that can be split into rectangles.
Split the compound shape into simpler shapes (usually rectangles), find any missing side lengths, calculate the area of each part, then add or subtract those areas to match the diagram. Always label each rectangle before you calculate.
Both methods work. Adding means partitioning the shape into two or more rectangles and summing their areas. Subtracting means treating the compound shape as a larger rectangle with a smaller rectangle removed. Choose the method that needs fewer missing lengths for that diagram.
Use the labelled sides. Horizontal lengths along the same run must add up to the overall width. Vertical lengths along the same run must add up to the overall height. Write the missing length on the diagram before you calculate any areas.
A reverse question gives the total area and asks you to find an unknown length. Split the shape as usual, write an equation using the unknown length, then solve. These questions appear regularly on GCSE Higher and Foundation papers.
Clear partitioning shows you understand the method and makes follow-through marks available if an arithmetic slip occurs later. Candidates who leave the diagram unlabelled are much more likely to use the wrong dimensions.
Download the free PDF worksheet from this page. It contains exam-style compound area questions with worked solutions, and is suitable for classwork, homework or independent revision.
Build a coherent perimeter and area sequence with these related resources. For the full curriculum, visit the Perimeter and Area hub.
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