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Area of a trapezium Quiz

Grade 4 • 4Y • 10 Questions (37 Marks)

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Score: 0 / 10
Area of a trapezium — Notes & Worked Examples Show / Hide

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
Question 1 IGCSE Jun 2022 2FR Q13
[2 marks]
The diagram shows a trapezium.
6 m3 m13 mDiagram NOTaccurately drawn
Work out the area of the trapezium.
m²
Worked Solution & Answer
(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
Question Paper (PDF) • Mark Scheme (PDF)
Question 2
[2 marks]
Here is a trapezium drawn on a centimetre grid.
On the grid, draw a triangle equal in area to this trapezium.
Worked Solution & Answer
Area of trapezium = 1/2 × (2 + 7) × 4 = 18 cm² M1
For a triangle of area 18 cm², 1/2 × base × height = 18 ⇒ base × height = 36 (e.g. base = 6, height = 6). A1
Answer: Any triangle drawn with area 18 cm² (e.g. base 6 cm and height 6 cm, or base 9 cm and height 4 cm)
Question Paper (PDF) • Mark Scheme (PDF)
Question 3 AQA Nov 2020 2H Q13
[3 marks]
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.
Answer m
Worked Solution & Answer
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
Question Paper (PDF) • Mark Scheme (PDF)
Question 4
[3 marks]
ABC and AED are straight lines.
BE and CD are parallel.
ABCDE
BE = 4.2 cm
CD = 6.3 cm
AC = 10.8 cm
Work out the area of trapezium BCDE.
cm²
Worked Solution & Answer
(The area of a trapezium is ½(a + b) × height)
Scale factor = 6.3 / 4.2 = 1.5 ⇒ AB = 10.8 ÷ 1.5 = 7.2 cm ⇒ BC = 10.8 – 7.2 = 3.6 cm M2
Area of trapezium BCDE = 1/2 × (4.2 + 6.3) × 3.6 = 18.9 cm² A1
Answer: 18.9 cm²
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Jan 2022 1F Q13
[4 marks]
The diagram shows a classroom wall in the shape of a trapezium.
2.5 m3.5 m6.5 mDiagram NOTaccurately drawn
Dion wants to paint the classroom wall completely twice.
He knows that each tin of paint will cover 12 m2
He is going to have to buy all the paint he needs.
Work out the least number of tins of paint that Dion will need to buy.
Show your working clearly.
Worked Solution & Answer
Area of wall = ½ × (2.5 + 3.5) × 6.5 = 3 × 6.5 = 19.5 m² M2
Area to paint twice = 2 × 19.5 = 39 m² M1
Number of tins = 39 ÷ 12 = 3.25 ⇒ 4 tins A1
Answer: 4
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 IGCSE Jun 2023 2HR Q5 / 2FR Q20
[4 marks]
A field is in the shape of a trapezium.
170 m330 m240 mDiagram NOTaccurately drawn
The field is sold for a price of \$49 650
Given that 1 hectare = 10 000 m2
work out the average price of the field per hectare.
$
Worked Solution & Answer
Area of trapezium = ½ × (170 + 330) × 240 = 250 × 240 = 60 000 m² M2
Number of hectares = 60 000 ÷ 10 000 = 6 hectares M1
Price per hectare = 49 650 ÷ 6 = $8275 A1
Answer: $ 8275
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 AQA Jun 2019 2H Q19
[4 marks]
Not drawnaccurately64°11 cm15 cm
Work out the area of the trapezium.
Answer cm²
Worked Solution & Answer
Difference between parallel sides = 15 - 11 = 4 cm M1
In the right-angled triangle on the left: M1
\tan 64° = h4 ⇒ h = 4 \tan 64° = 4 × 2.0503 = 8.2012 cm M1
Area of trapezium = a + b2 × h = 11 + 152 × 8.2012 = 13 × 8.2012 = 106.616… cm2 or 107 or 106.6. A1
Answer: Answer 107 cm²
Question Paper (PDF) • Mark Scheme (PDF)
Question 8 IGCSE Nov 2020 2F Q13
[5 marks]
The diagram shows the plan of Sophia's gym floor.
20 m12 m26 mDiagram NOTaccurately drawnSpecial Offer1 tin for $134 tins for $40
Sophia is going to paint all the gym floor.
Each tin of paint she is going to use covers an area of 20 m2
There is a special offer on the paint that Sophia is going to buy.
Work out the least amount of money that Sophia has to pay in order to buy all the paint she needs.
Show your working clearly.
$
Worked Solution & Answer
Area of trapezium = ½ × (20 + 26) × 12 = 276 m² M2
Tins needed = 276 ÷ 20 = 13.8 → 14 tins M2
Cheapest way to buy 14 tins: 3 × 4-tin offers ($120) + 2 single tins (2 × $13 = $26) = $146 A1
Answer: $ 146
Question Paper (PDF) • Mark Scheme (PDF)
Question 9
[5 marks]
The diagram shows a floor in the shape of a trapezium.
10 m16 m7 m5 litres£16.99
John is going to paint the floor.
Each 5 litre tin of paint costs £16.99
1 litre of paint covers an area of 2 m2
John has £160 to spend on paint.
Has John got enough money to buy all the paint he needs?
You must show how you get your answer.
Worked Solution & Answer
(The area of a trapezium is ½(a + b) × height)
Area = ½ × (10 + 16) × 7 = 91 m² M2
Litres needed = 91 ÷ 2 = 45.5 litres M1
Tins needed = 45.5 ÷ 5 = 9.1 → 10 tins M1
Cost = 10 × £16.99 = £169.90 > £160, so No. A1
Answer: No — area is 91 m², needing 45.5 litres = 10 tins costing £169.90, which is more than £160
Question Paper (PDF) • Mark Scheme (PDF)
Question 10 Specimen Set 1 3F Q25 / 3H Q5
[5 marks]
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 & Answer
(a)
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
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 37 marks)
Area of a trapezium Worksheets Next: Loci and construction →

Grade 4 Quizzes

24 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