Where can I download free area of compound shapes PDF worksheets with answers?

On this MathsLinks page you can download free printable area of compound shapes PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Corbett Practice, Corbett Textbook, Maths Made Easy, plus a printable one-page area of compound shapes revision guide.

What GCSE grade is area of compound shapes (3X)?

Area of compound shapes (topic code 3X) is a Grade 3 geometry topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Area of compound shapes Worksheets (PDF) with Answers — GCSE Maths

Free Area of compound shapes PDF Worksheets & Answers

Grade 3 • Topic 3X

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Dr Frost (B. Blocks) Building Blocks skill sheet & answers	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
Maths4EveryOne KS2 SATs questions & solutions	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 3 topics
3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables

Explanation:

A compound (composite) shape is made up of two or more simple shapes joined together. To find its area, draw a dotted line to split it into rectangles or triangles, work out any missing side lengths first by comparing parallel horizontal and vertical sides, and then add the separate areas together.

Remember the key area formulas: Rectangle = length × width, and Triangle = 12 × base × perpendicular height. For shaded region questions, calculate the outer area minus the unshaded inner area.

Example 1: An L-shape has total width 10 cm, total height 8 cm, top width 4 cm, and right height 3 cm. Find its area.

Left = 4 × 8 = 32 cm²

Right = (10−4) × 3 = 18 cm²

Total = 32 + 18 = 50 cm²

Example 2: A pentagon has a 6 m by 4 m rectangular base and a triangle on top. Total height is 7 m. Find the area.

Rect = 6 × 4 = 24 m²

Tri h = 7 − 4 = 3 m

Tri = 12×6×3 = 9 m² → 33 m²

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Area of compound shapes Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jun 2021 1F Q18 / 1H Q3 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

The diagram shows the shape ABCDE.
The area of the shape is 91.8 cm²

Work out the value of x.

Worked Solution & Mark Scheme (4 marks)

14x + ½ × 6 × (13 − x) = 11x + 39 = 91.8 M2
⇒ 11x = 52.8 M1
⇒ x = 4.8 A1

Answer: x = 4.8

Past Paper Example 2 Specimen Set 1 1F Q23 / 1H Q4 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

A pattern is made using identical rectangular tiles.

Find the total area of the pattern.

Worked Solution & Mark Scheme (4 marks)

Let length = l and width = w. l + w = 7 and 2l + w = 11 ⇒ l = 4 cm, w = 3 cm M2
Area of 1 tile = 4 × 3 = 12 cm² M1
Total area = 4 × 12 = 48 cm². A1

Answer: 48 cm²

Past Paper Example 3 IGCSE Jun 2025 1F Q17 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

The diagram shows the plan of a stage.
The stage is made up of a rectangle and an isosceles triangle.

Yuko is going to cover the stage with varnish.
She needs to buy enough tins of varnish to cover the stage with one coat of varnish.
Each tin of varnish covers an area of 4 m²
Work out the smallest number of tins of varnish that Yuko needs to buy.
Show your working clearly.

Worked Solution & Mark Scheme (4 marks)

Rectangle area = 6 × 8 = 48 m² M1
Triangle area = ½ × 6 × 3 = 9 m² M1
Total area = 48 + 9 = 57 m² M1
57 ÷ 4 = 14.25 ⇒ 15 tins A1

Answer: 15

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