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Area of a trapezium

Free Printable Area of a trapezium PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 4)

Download free area of a trapezium worksheets (PDF), GCSE maths past paper questions and worked solutions for Area of a trapezium (4Y). This is a Grade 4 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Corbett Maths, Dr Frost, Maths DIY, TES Resource, Dr Austin, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our area of a trapezium revision notes and worked examples with diagrams, try real GCSE past paper area of a trapezium questions with step-by-step solutions, or download a PDF of all area of a trapezium worksheet links.

Free Area of a trapezium PDF Worksheets & Answers

Grade 4 • Topic 4Y
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Practice Questions & answers
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Textbook Exercise & answers
 Qs Ans
GCSE worksheet & solutions
 Qs Ans
Exam-style booklet & solutions
 Qs Ans
TES Resource
Area of a trapezium questions & answers
 Qs Ans
Practice grid / worksheet & answers
 Qs Ans
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
Interactive online lesson & practice
 Page
Self-marking online worksheet
 Page
Grade 4 topics
4A - Compound interest4B - Indices (index laws)
4C - Prime factors HCF and LCM4D - Real life graphs
4E - Inequalities on a number line4F - Solving inequalities
4G - Forming and solving equations4H - nth term of a linear sequence
4J - Expanding and factorising4K - Pythagoras theorem
4L - Angles in parallel lines4M - Angles in polygons
4N - Surface area4P - Volume of a cuboid
4Q - Volume of a prism4R - Bearings
4S - Cylinders4T - Plans and elevations
4U - Scatter graphs4V - Probability
4W - Averages from tables4X - Reverse mean
4Y - Area of a trapezium4Z - Loci and construction
GCSE Maths Grade 4 Revision Notes & Method

Guide to Area of a trapezium: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A trapezium is a quadrilateral with one pair of parallel sides (labelled a and b). Its area is given by the formula: Area = a + b2 × h (half the sum of the parallel sides, multiplied by the perpendicular height h between them).

Always add the two parallel sides (a + b) first before dividing by 2 and multiplying by h. Never use a sloping side as the height h!

Example 1: Calculate the area of the trapezium below.

7 cm 11 cm 6 cm
Area = 7 + 112 × 6 = 9 × 6 = 54 cm²
Answer: 54 cm²

Example 2: A trapezium has an area of 60 cm², parallel sides of 9 cm and 15 cm, and perpendicular height h cm. Find h.

Solution:

Substitute into Area = a + b2 × h:
9 + 152 × h = 60 → 12h = 60
Divide by 12: h = 60 ÷ 12 = 5
Answer: h = 5 cm
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Area of a trapezium Questions & Answers

Past Paper Example 1 AQA Nov 2020 2H Q13 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a wall.
The area of the wall is 39.2 m2
Not drawnaccurately2.8 m2.1 mlength
Work out the length of the wall.
Worked Solution & Mark Scheme (3 marks)
The wall is a right-trapezium with parallel heights 2.8 m and 2.1 m: M1
Area = 2.8 + 2.12 × length = 2.45 × length M1
2.45 × length = 39.2 ⇒ length = 39.22.45 = 16 m. A1
Answer: Answer 16 m
Past Paper Example 2 Specimen Set 1 3F Q25 / 3H Q5 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a wall in the shape of a trapezium.
1.8 m2.7 m0.8 m
Karen is going to cover this part of the wall with tiles.
Each tile is rectangular, 15 cm by 7.5 cm
Tiles are sold in packs.
There are 9 tiles in each pack.
Karen divides the area of this wall by the area of a tile to work out an estimate for the number of tiles she needs to buy.
(a) Use Karen's method to work out the estimate for the number of packs of tiles she needs to buy. [5 marks]
Worked Solution & Mark Scheme (5 marks)
Part (a) Solution:
Area of wall = ½(180 + 270) × 80 = 18 000 cm² M2
Area of 1 tile = 15 × 7.5 = 112.5 cm² M1
Number of tiles = 18 000 ÷ 112.5 = 160 tiles M1
Packs = 160 ÷ 9 = 17.77... → 18 packs A1
Answer (a): 18
Past Paper Example 3 IGCSE Jun 2022 2FR Q13 2 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a trapezium.
6 m3 m13 mDiagram NOTaccurately drawn
Work out the area of the trapezium.
Worked Solution & Mark Scheme (2 marks)
(The area of a trapezium is ½(a + b) × height)
Area = ½ × (6 + 13) × 3 = ½ × 19 × 3 = 28.5 m² M1 A1
Answer: 28.5 m²

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