Measurement and geometry • using Units of measurement
10e
Area of trapeziums
■■
A trapezium is a quadrilateral with one pair of parallel sides.
The following figures are all trapeziums.
■■
The height of the trapezium is perpendicular to each of its parallel bases.
eBook plus
Digital doc
Investigation
Area of a
trapezium
doc-2320
a
h
b
To determine the area of a trapezium, draw two lines to create two triangles and one rectangle as
shown.
a
h
a
h
h
h
b–a
■■
Placing the two triangles together creates one triangle and one rectangle.
1
The total area of the two shapes, A, will give A = a ì h + 2 ì h ì (b - a).
1
Simplifying this gives A = 2 (a + b) ì h.
1
The area of a trapezium, A, is given by the formula A = 2 (a + b) ì h, where a and b are the
lengths of parallel sides and h is the height of the trapezium.
Worked Example 12
Find the area of the trapezium at right.
6 cm
4 cm
10 cm
Think
1
262
Write the formula for the area of the trapezium.
Maths Quest 8 for the Australian Curriculum
Write
1
A = 2 (a + b) ì h
Measurement and geometry • using Units of measurement
2
Identify the values of a, b and h.
Note: It does not matter which of the parallel sides is a
and which one is b, since we will need to add them together.
a = 10, b = 6 and h = 4
3
Substitute the values of a, b and h into the formula.
A = 2 ì (10 + 6) ì 4
4
Evaluate (work out the brackets first) and include the
correct units.
A = 2 ì 16 ì 4
1
1
= 32 cm2
remember
1
The area of a trapezium is given by the formula A = 2 (a + b) ì h, where a and b are
parallel sides and h is the height of a trapezium.
a
h
b
The height of the trapezium is always perpendicular to the parallel sides.
Exercise
10E
Individual
Pathways
eBook plus
Area of trapeziums
fluency
1 WE 12 Find the area of each of the following trapeziums.
b
a
3 cm
Activity 10-E-1
2 cm
Area of a trapezium
doc-2309
More trapeziums
doc-2310
Advanced trapeziums
doc-2311
4.5 m
6 cm
Activity 10-E-2
Activity 10-E-3
9m
6m
c
d
5.0 m
14 mm
18 mm
3.0 m
25 mm
3.5 m
e
8.0 cm
0.9 cm
2.4 cm
f
50 m
48 m
80 m
Chapter 10 Measurement
263