Area of a trapezium

The Maths Habit

1 Work out the area of the rectangle.

7 cm4 cm
28 cm2

2 What is half of 50?

25

3 Work out the area of the triangle.

6 cm4 cm
12 cm2

A rectangle is cut into two pieces. Which piece is bigger, A or B?

BA

Neither. A turned round fits on B. Each is half.

Trapezium
A shape with four straight sides. Two of them are parallel.
Parallel
Lines that stay the same distance apart. They never meet.
Perpendicular height
How tall the shape is, measured at a right angle to the parallel sides.
Right angle
A square corner. It is a quarter turn.

heighttopbottom
  1. Add the two parallel sides.Top + bottom.
  2. Two trapeziums make a rectangle.Times by the height.
  3. The trapezium is half the rectangle.Divide by 2.
  4. Write the units.Area is in square units: cm².
Addtop+bottom=
Rectangle×height=
Half÷ 2 =
Areacm²

Work out the area.

4 cm2 cm6 cm
Add2+6=8
Rectangle8×4=32
Half32÷ 2 =16
Area16cm²

Work out the area.

3 cm3 cm5 cm
Add3+5=8
Rectangle8×3=24
Half24÷ 2 =12
Area12cm²

Work out the area.

4 cm2 cm6 cm
Add2+6=8
Rectangle8×4=32
Half32÷ 2 =16
Area16cm²

Work out the area.

3 cm4 cm6 cm
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²
Add4+6=10
Rectangle10×3=30
Half30÷ 2 =15
Area15cm²

Work out the area.

4 cm2 cm6 cm
Add2+6=8
Rectangle8×4=32
Half32÷ 2 =16
Area16cm²

Work out the area.

6 cm2 cm4 cm
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²
Add2+4=6
Rectangle6×6=36
Half36÷ 2 =18
Area18cm²

Work out the area.

4 cm2 cm6 cm
Add2+6=8
Rectangle8×4=32
Half32÷ 2 =16
Area16cm²

Work out the area.

6 cm3 cm7 cm
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²
Add3+7=10
Rectangle10×6=60
Half60÷ 2 =30
Area30cm²

Work out the area of each trapezium.

15 cm2 cm6 cm
Add2+6=8
Rectangle8×5=40
Half40÷ 2 =20
Area20cm²
26 cm3 cm5 cm
Add3+5=8
Rectangle8×6=48
Half48÷ 2 =24
Area24cm²
34 m3 m4 m
Add3+4=7
Rectangle7×4=28
Half28÷ 2 =14
Area14m²
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²

Which two sides are parallel?

ACDBA and C

Which line is the perpendicular height?

BDEACB

heighttopbottom
  1. The height is the dashed line.It meets the parallel sides at a right angle.
  2. Slide the striped piece to the other end.The two trapeziums make a rectangle again.
  3. Use the same frame.Add, rectangle, half, area.

Work out the area.

5 cm4 cm6 cm
Add4+6=10
Rectangle10×5=50
Half50÷ 2 =25
Area25cm²

Work out the area.

5 cm2 cm6 cm
Add2+6=8
Rectangle8×5=40
Half40÷ 2 =20
Area20cm²

Work out the area.

5 cm4 cm6 cm
Add4+6=10
Rectangle10×5=50
Half50÷ 2 =25
Area25cm²

Work out the area.

4 cm3 cm5 cm
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²
Add3+5=8
Rectangle8×4=32
Half32÷ 2 =16
Area16cm²

Work out the area.

5 cm4 cm6 cm
Add4+6=10
Rectangle10×5=50
Half50÷ 2 =25
Area25cm²

Work out the area.

7 cm4 cm6 cm
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²
Add4+6=10
Rectangle10×7=70
Half70÷ 2 =35
Area35cm²

Work out the area.

5 cm4 cm6 cm
Add4+6=10
Rectangle10×5=50
Half50÷ 2 =25
Area25cm²

Work out the area.

8 cm3 cm7 cm
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²
Add3+7=10
Rectangle10×8=80
Half80÷ 2 =40
Area40cm²

Work out the area of each trapezium.

16 cm3 cm5 cm
Add3+5=8
Rectangle8×6=48
Half48÷ 2 =24
Area24cm²
25 cm3 cm7 cm
Add3+7=10
Rectangle10×5=50
Half50÷ 2 =25
Area25cm²
36 m4 m6 m
Add4+6=10
Rectangle10×6=60
Half60÷ 2 =30
Area30m²
heighttopbottomAdd top + bottomRectangle × heightHalf ÷ 2Area in cm²

Is the area right? Thumbs up or thumbs down.

A4 cm2 cm6 cmArea = 16 cm2Right
B4 cm3 cm5 cmArea = 32 cm2Wrong: 16 cm2
C3 cm4 cm6 cmArea = 15 cm2Right
D5 cm2 cm4 cmArea = 30 cm2Wrong: 15 cm2

Area of a Trapezium worksheet, page 1

Area of a Trapezium worksheet, page 2

Answer sheet

  1. Two trapeziums fit together to make a rectangle 10 cm long and 5 cm tall. What is the area of one trapezium?

    25 cm2

  2. A trapezium has parallel sides of 3 cm and 6 cm. Its height is 5 cm. Work out its area.

    22.5 cm2

  3. A trapezium has parallel sides of 3 cm and 7 cm. Its area is 20 cm². How tall is it?

    4 cm

  1. Work out the area. Add2+6=8Rectangle8×5=40Half40÷ 2 =20

    Area = 20 cm2
    5 cm2 cm6 cm

  2. Work out the area. Add3+5=8Rectangle8×6=48Half48÷ 2 =24

    Area = 24 cm2
    6 cm3 cm5 cm

  3. Work out the area.

    15 cm2
    3 cm2 cm8 cm
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