MeasureMent and geoMetry • Using Units of MeAsUreMent
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In many situations the area of a given shape can be found by subtracting individual areas from
each other.
If a shaded area is required, the total area is found first and then the area of the ‘unshaded’
part(s) is subtracted from it.
WorKed eXaMPLe 13
Find the shaded area in the figure below.
5m
2m
tHinK
Write
1
The figure shown is a large square from which a
small square has been removed. Write the formula
for the area of the square.
Area of a square = l2
2
Calculate the area of the large square first.
3
Calculate the area of the small square.
Large square: A = 52
= 25 m2
Small square: A = 22
= 4 m2
4
Now find the shaded area by subtracting the area of
the small square from that of the large one.
Shaded area = 25 - 4
= 21 m2
reMeMBer
1. Many composite shapes can be divided into two or more ‘pieces’ which have a simple
area formula.
2. The area of a composite shape can be found by adding together the areas of each part
the shape is divided into.
3. Many problems such as finding a shaded area can be solved by subtracting one area
from another.
eXerCise
9e
inDiviDUAl
PatHWays
eBoo
k plus
eBook
Activity 9-E-1
Composite shapes
doc-1867
Activity 9-E-2
More composite
shapes
doc-1868
324
Area of composite shapes, using addition
and subtraction
flUenCY
1 We12 Find the area of the following composite shapes.
a
b
1m
2m
12 cm
6 cm
9 cm
Maths Quest 7 for the Australian Curriculum
4m
MeasureMent and geoMetry • Using Units of MeAsUreMent
inDiviDUAl
PatHWays
c
d
3 cm
2 cm
eBoo
k plus
eBook
5 cm
Activity 9-E-3
8 cm
4 cm
2 cm
Advanced composite
shapes
doc-1869
8 cm
e
f
28 cm
14 cm
1.5 m
6m
14 cm
28 cm
eBoo
k plus
eBook
Digital docs
4 cm
3m
2 We13 Find the area of the following shapes.
a
10 m
b
25 m
5m 5m
5m
6m
Spreadsheet
Area
2m
doc-1878
6m
5m
5m
UnDerstAnDing
3 The sail whose measurements are shown at right has been constructed
for the sailing vessel Nautilus.
a Find the area of cloth required to construct the sail.
b What is the cost of the sail if the cloth costs $12.00 per square
metre?
4 a Find the area of carpet needed
for the room at right.
b What would the carpet for the
6.0 m
room cost if it is sold for $25
4.5 m
per square metre?
3.0 m
5 Find the area of the garage wall
4.5 m
shown below.
7.5 m
6.3 m
1.0 m
2.4 m
4.5 m
6 Determine the area of bricks needed to cover the courtyard shown below.
8m
5m
1.2 m
1.2 m
7 A sheet of A4 paper is approximately 30 cm long and 21 cm wide. Find the area of the triangle
formed by cutting an A4 sheet in half diagonally.
Chapter 9
Measurement
325
MeasureMent and geoMetry • Using Units of MeAsUreMent
8 Find the area of the entrance foyer shown on the right.
2m
9 Michael is paving a rectangular yard, which is 15.5 m long and
8.7 m wide. A square fishpond with side lengths of 3.4 m is in the
centre of the yard. What will be the cost of paving Michael’s yard,
if the paving material costs $17.50 per square metre?
10 Members of the Lee family want to pave the area around
their new swimming pool. The pool is set into the corner of
the yard as shown at right. Find the area of paving (in square
metres) required to cover the yard around the pool (shaded in the
diagram).
14 m
Pool 4.5 m
3m
3.5 m
6m
6m
2m
11 In order to construct an advertising sign, the letters below are cut from plastic sheets. Find the
total area of plastic required to make all 3 letters.
4m
2m
2m
2m
4m
1m
1m
2m
2m
2m
4m
refleCtion
How will you decide whether
to find the area of a given
composite shape by addition or
by subtraction?
9f
volume
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The volume of a 3-dimensional object is the amount of space it occupies.
Volume is measured in cubic units such as mm3, cm3, m3, etc.
A cubic centimetre (cm3) is the space occupied by a cube with sides of 1 cm.
A sugar cube has a volume of about 1 cm3.
326
Maths Quest 7 for the Australian Curriculum
The volume of a discman is about 30 cm3.