GCSE MATHS • HIGHER TIER
Compound Shapes Made Simple
Learn how to split compound shapes into simpler shapes, calculate each area, and add or subtract areas to find the total area.
Clear method
Exam practice
Worked proofs
Compound Shapes in Six Moves
1
Identify
Identify all the simple shapes that make up the compound shape.
2
Split
Split the compound shape carefully into simpler sections.
3
Calculate
Calculate the area of each section separately.
4
Add or Subtract
Add areas for joined sections or subtract any missing sections.
5
Check
Check the calculations carefully.
6
Units
Include the correct square units in the final answer.
What You’ll Learn
Recognise compound shapes
Understand that a compound shape is formed by joining two or more simple shapes.
Understand area
Know that area measures the space inside a two-dimensional shape and is measured in square units.
Split complex shapes
Break a compound shape into rectangles, triangles, semicircles, trapeziums or other simple shapes.
Combine areas
Calculate each section and add or subtract the areas as required.
Key Rules
Split into simple shapes
Break the compound shape into shapes whose areas you can calculate.
Use the correct area formula
Apply the correct formula for each rectangle, triangle, circle, semicircle or trapezium.
Add joined sections
Add the individual areas when the parts make up the whole shape.
Subtract missing sections
Subtract the area of a hole or removed section from the larger area.
Worked Proof: Two Rectangles
Question: A compound shape consists of two rectangles.
1. Identify
Rectangle A: 8 cm × 4 cm
Rectangle B: 5 cm × 3 cm
2. Calculate Rectangle A
Area A = 8 × 4 = 32 cm²
3. Calculate Rectangle B
Area B = 5 × 3 = 15 cm²
4. Add the Areas
Total Area = 32 + 15 = 47 cm²
More Worked Examples
1
Rectangle and Triangle
Question: A rectangle measures 10 cm × 6 cm. A triangle with base 8 cm and height 5 cm is attached.
Rectangle Area = 10 × 6 = 60 cm²
Triangle Area = ½ × 8 × 5 = 20 cm²
Total Area = 60 + 20 = 80 cm²
Triangle Area = ½ × 8 × 5 = 20 cm²
Total Area = 60 + 20 = 80 cm²
2
Rectangle and Semicircle
Question: A shape consists of a rectangle measuring 12 cm × 5 cm and a semicircle with radius 3 cm.
Rectangle Area = 12 × 5 = 60 cm²
Semicircle Area = ½ × π × 3² ≈ 14.14 cm²
Total Area ≈ 60 + 14.14 = 74.14 cm²
Semicircle Area = ½ × π × 3² ≈ 14.14 cm²
Total Area ≈ 60 + 14.14 = 74.14 cm²
3
L-Shaped Figure
Question: An L-shaped figure can be split into two rectangles.
Rectangle A = 7 × 4 = 28 cm²
Rectangle B = 3 × 5 = 15 cm²
Total Area = 28 + 15 = 43 cm²
Rectangle B = 3 × 5 = 15 cm²
Total Area = 28 + 15 = 43 cm²
4
Missing Rectangle
Question: A large rectangle measures 15 cm × 10 cm. A smaller rectangle measuring 5 cm × 4 cm is removed..
Large Area = 15 × 10 = 150 cm²
Small Area = 5 × 4 = 20 cm²
Compound Area = 150 − 20 = 130 cm²
Small Area = 5 × 4 = 20 cm²
Compound Area = 150 − 20 = 130 cm²
- Common GCSE Mistakes
- Incorrect splitting: Split the compound shape into suitable simple shapes.
- Wrong formula: Use the correct area formula for each section.
- Missing subtraction: Subtract holes or removed sections when required.
- Arithmetic errors: Check each individual area calculation.
- Missing units: Write the final area in square units.
- Exam Tips
- Draw dividing lines: Use them to visualise simpler sections.
- Revise area formulae: Know rectangles, triangles, trapeziums and circles.
- Check add or subtract: Decide how the sections combine before calculating.
- Practise exam-style questions: Use a variety of compound-shape problems.
- Check your answer: Review calculations and square units before finishing.
Skills Used in Compound Shapes
Circles
Surface Area
Volume of Prisms
Similar Shapes
Scale Drawings
Mensuration
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Compound Shapes Tutorial
Step-by-step walkthroughs of Compound Shapes with clear methods and exam tips.
Frequently Asked Questions
Area measures the amount of space inside a two-dimensional shape and is written in square units.
Split the shape into simpler shapes, calculate each area, then combine the areas.
Subtract when the compound shape contains a hole or a missing section.
Revise rectangles, triangles, circles and semicircles, and trapeziums because these can appear inside compound shapes.
