GCSE Maths / Edexcel

Compound area

Find the area of compound shapes by choosing a clear split, finding missing lengths, and adding or subtracting simple areas accurately.

Geometry and MeasuresFoundation and HigherGrades 4 to 6Focused skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Compound area

Pearson Edexcel GCSE Maths geometry G9: calculate area of compound shapes using known formulae.

Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

A compound shape is made from two or more simpler shapes.

The safest method is to split the shape into rectangles, triangles or trapezia that you already know how to calculate.

Sometimes it is easier to find a large outer rectangle and subtract the missing piece.

Before finding area, calculate any missing lengths from the diagram. Opposite horizontal or vertical lengths often help.

Label each part clearly. Edexcel method marks often reward a correct split even if one arithmetic step is wrong.

For L-shapes, check whether your split creates two rectangles with no overlap. If they overlap, you may count part of the shape twice.

For cut-out shapes, find the area of the full outer rectangle first, then subtract the missing rectangle.

Write units at the end. Compound area still uses square units.

Key ruleSplit, calculate each simple area, then add or subtract.

Diagram guide

ABsplit into rectangles10 cm8 cm
Split an L-shapeDraw a split line to turn the compound shape into rectangles, then add the rectangle areas.
outer areacut outlarge rectanglearea left = outer area - cut out area
Subtract a missing rectangleWhen a corner has been removed, it can be easier to find the large outer area and subtract the cut-out.
total 12 cm5 cmxleft rectangletop rectanglemissing length: x = 12 - 5
Missing lengths firstMany exam questions hide one side length. Use total lengths and known parts before calculating area.

Worked examples

Add two rectangles

An L-shape is split into rectangles with areas 30 cm² and 18 cm². Find the total area.

ABsplit into rectangles10 cm8 cm
Example: split and addIf the two rectangles do not overlap, add their areas.
  1. Add the two rectangle areas.
  2. 30 + 18 = 48.

Answer: 48 cm²

Find a missing length

A total width is 12 cm. One horizontal part is 5 cm. Find the missing horizontal length.

total 12 cm5 cmxleft rectangletop rectanglemissing length: x = 12 - 5
Example: missing sideThe two horizontal parts together make the total width.
  1. The two horizontal parts make the total width.
  2. 12 - 5 = 7.

Answer: 7 cm

Subtract method

A 10 cm by 8 cm rectangle has a 3 cm by 4 cm corner removed. Find the area left.

outer areacut outlarge rectanglearea left = outer area - cut out area
Example: outer area minus cut-outFind the full rectangle first, then subtract the removed corner.
  1. Outer rectangle area = 10 x 8 = 80.
  2. Removed rectangle area = 3 x 4 = 12.
  3. Area left = 80 - 12.

Answer: 68 cm²

Choose the easier method

A compound shape is a 12 cm by 9 cm rectangle with a 4 cm by 3 cm rectangle removed. Explain the best method.

outer areacut outlarge rectanglearea left = outer area - cut out area
Example: choose the methodA missing corner usually makes the subtraction method quicker.
  1. The full rectangle is easy to calculate.
  2. The removed rectangle is also easy to calculate.
  3. Use outer area - removed area.

Answer: Use the subtract method: 12 x 9 - 4 x 3.

Common mistakes

  • Adding all side lengths instead of finding area.
  • Forgetting to find a missing length before multiplying.
  • Double-counting the overlap between two split rectangles.
  • Subtracting the wrong rectangle in the outer-area method.
  • Finding perimeter when the question asks for area.
  • Leaving the answer without square units.

Quick exercise

Try these before moving to the exam-style questions.

  1. A compound shape is split into areas 24 cm² and 35 cm². Find the total area.
    ABsplit into rectangles10 cm8 cm
    Quick check: split and addAdd the two non-overlapping areas.
  2. A 9 by 6 rectangle has a 2 by 3 corner removed. Find the area left.
    outer areacut outlarge rectanglearea left = outer area - cut out area
    Quick check: subtract cut-outOuter area minus removed area.
  3. A total length is 14 cm and one part is 6 cm. Find the missing part.
    total 12 cm5 cmxleft rectangletop rectanglemissing length: x = 12 - 5
    Quick check: missing lengthUse the total length before area.
  4. Two rectangles have areas 45 cm² and 12 cm². Find the combined area.
    ABsplit into rectangles10 cm8 cm
    Quick check: combined areaCheck the rectangles do not overlap, then add.
  5. A 12 by 10 rectangle has a 5 by 4 rectangle removed. Find the area left.
    outer areacut outlarge rectanglearea left = outer area - cut out area
    Quick check: large rectangle minus small rectangleCalculate both areas before subtracting.
Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationCalculator3 marks

An L-shape is split into two rectangles. Their areas are 28 cm² and 36 cm². Work out the total area.

ABsplit into rectangles10 cm8 cm
Question diagram: add component areasThe split has already been done, so add the two rectangle areas.
compound areaadding areasfoundation geometry
Standard exam styleFoundation and HigherCalculator4 marks

A rectangle measuring 13 cm by 9 cm has a 4 cm by 5 cm rectangle cut out. Work out the remaining area.

outer areacut outlarge rectanglearea left = outer area - cut out area
Question diagram: remaining areaUse outer rectangle area minus cut-out rectangle area.
compound areasubtract areamethod marks
ChallengeFoundation and HigherEither5 marks

An L-shape has a left rectangle 4 cm by 11 cm and a top rectangle 9 cm by 3 cm. The two rectangles do not overlap. Work out the total area.

ABsplit into rectangles10 cm8 cm
Question diagram: two-rectangle splitFind each rectangle area, then add because the question says they do not overlap.
compound areasplitting shapesdiagram reasoning