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GCSE Maths · Higher · Chapter 9: Length, area and volume · Lesson 2

Parallelograms and trapezia

Grades 4–7About 50 minutesCalculator allowed37 marks
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NameClassDate
A

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

  1. A1
    Needed today

    Find the area of a triangle with base cm and height cm.

    [1 mark]
    Answer
  2. A2
    Last lesson

    A circle has diameter 16 cm. Find its area in terms of .

    [1 mark]
    Answer
  3. A3
    Key Stage 3

    Work out of .

    [1 mark]
    Answer
  4. A4
    Key Stage 3

    Write in its simplest form.

    [1 mark]
    Answer
B

Example, then your turn

Grades 4–5

Your teacher works through each example with you. Then try the one beside it.

Example 1

Work out the area of the parallelogram.

11 cm7 cm6 cm
  1. B1

    Work out the area.

    [2 marks]
    14 cm6 cm5 cm
    Answer
Example 2

Work out the area of the trapezium.

13 cm7 cm5 cm
  1. B2

    Work out the area.

    [2 marks]
    13.5 cm9.5 cm4 cm
    Answer
C

Practice

Grades 5–7
  1. C1

    A trapezium has area cm and perpendicular height cm. One parallel side is cm. Work out the other parallel side.

    [2 marks]
    Answer
  2. C2

    The rectangle is cm by cm. What percentage of it is shaded?

    [3 marks]
    4 cm4 cm
    Answer
  1. C3

    The trapezium has two equal sloping sides. Work out its area.

    [3 marks]
    18 cm8 cm13 cm13 cm
    Not drawn accurately
    Answer
  2. C4

    The parallelogram and the trapezium have the same area. Work out the value of .

    [3 marks]
    (x + 7) cm4 cm(x + 4) cmx cm6 cm
    Not drawn accurately
    Answer
  3. C5

    A floor of area m is covered with tiles like this one. How many tiles are needed?

    [3 marks]
    30 cm20 cm
    Answer
  4. C6

    is a trapezium with corners , , and . Work out its area.

    [2 marks]
    xy−3−2−1123456712345OABCD
    Answer
D

Exam-style questions

Grades 6–7
  1. D1

    is a parallelogram. cm and cm. The perpendicular distance between and is cm. Lena says, "The area of is cm."

    ABCD21 cm14 cm8 cm
    (a)

    Explain why Lena is wrong.

    [1 mark]
    (b)

    Work out the perpendicular distance between and .

    [3 marks]
    Answer
    Total for D1: 4 marks
  1. D2

    A lawn is a trapezium with a rectangular pond in it. Fertiliser is spread on the lawn but not on the pond, at g per m. Fertiliser is sold in kg boxes costing £ each. Work out the cost of the fertiliser needed. You must show your working.

    [5 marks]
    26 m18 m15 m4 m3 mpond
    Answer
E

Extension

Grade 7 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

  1. E1

    The trapezium has parallel sides of cm and cm and a perpendicular height of cm. The dashed line is parallel to them and halfway between them. It cuts the trapezium into two smaller trapezia. Work out the area of each part.

    [4 marks]
    15 cm7 cm3 cm3 cm
    Hint 1 · What to try

    Each part is a trapezium of height cm. You need the length of the dashed line.

    Hint 2 · The first line

    Halfway up, the width has changed by half of the change from cm to cm.

    Hint 3 · The full method

    The dashed line is cm. Now use for each part.

    Answer cm² and cm²
F

How did it go?

Colour one circle on each line.
Not yetNearlyYes
I can work out the area of a parallelogram and a trapezium, using the perpendicular height.
I can work back from an area to a missing length.
I can use these areas in compound shapes and problems with units and costs.

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