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Adding & Subtracting Areas (AQA GCSE Maths): Revision Note

Exam code: 8300

Naomi C

Written by: Naomi C

Reviewed by: Dan Finlay

Updated on

AQA Maths: FoundationOCR Maths: FoundationOCR Maths: HigherAQA Maths: HigherEdexcel Maths: FoundationEdexcel Maths: Higher

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Adding & Subtracting Areas

What is a compound shape?

  • Sometimes you will have a shape that is not a standard shape such as a rectangle, triangle, trapezium etc.

    • These are often called compound shapes

    • We can split the non-standard shape into standard shapes

How do I find the area of a compound shape?

  • Split the compound shape into standard shapes

  • Find the areas of the standard shapes

  • Add these areas together to find the area of the compound shape

  • Occasionally it may be easier to add an extra shape to the diagram and subtract the area of the extra shape from the new bigger shape

    • For the shape below you might complete the rectangle by putting a triangle in the top right corner

    • The area of the original shape is the rectangle minus the triangle

IGCSE & GCSE Maths revision notes

Examiner Tips and Tricks

Take a moment to think about how to split up the shape into the easiest shapes possible – there will probably be more than one way to do it!

Worked Example

Find the area of the pentagon shown in the diagram below.

Pukoyl43_edexcel-3-5-2-adding-and-subtracting-areas-we-diagram

Separate the diagram into two shapes that you are familiar with and know the area formulae for
This pentagon can easily be split into a rectangle and a triangle

Use the values given to find the length of the base and the height of the triangle and add these to the diagram. 

A compound shape split into standard shapes

The total area will be the area of the rectangle + the area of the triangle.

table row cell Total space area space end cell equals cell space open parentheses 12 cross times space 4 close parentheses space plus 1 half open parentheses 7 cross times 5 close parentheses end cell row blank equals cell space 48 plus 1 half open parentheses 35 close parentheses end cell end table

Area = 65.5 cm2

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Author
Reviewer
Naomi C

Author: Naomi C

Expertise: Maths Content Creator

Naomi graduated from Durham University in 2007 with a Masters degree in Civil Engineering. She has taught Mathematics in the UK, Malaysia and Switzerland covering GCSE, IGCSE, A-Level and IB. She particularly enjoys applying Mathematics to real life and endeavours to bring creativity to the content she creates.

Dan Finlay

Reviewer: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

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