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Length, Perimeter and Area

SERIES TOPIC

2 F 1

0 cm 51 6 102 7 113 8 12 14 154 9 13

Convert these lengths to metres:


Convert these lengths to centimetres:

Convert these lengths to millimetres:

Thisconversionboxcanhelpyou convertunitsoflength.

4

5

3

6

m mmcm

× 100

÷ 100

× 10

÷ 10

× 1 000

÷ 1 000

Units of length – m, cm, mm

To convert from mm to cm, divide by 10.

To convert from cm to mm, multiply by 10.

To convert from mm to m, divide by 1 000.

a 5cm = mm

d 7cm = mm

b 3 cm = mm

e 11 cm = mm

c 9cm = mm

f 15cm= mm

a 50mm = cm

d 15mm = cm

b 20 mm = cm

e 156mm = cm

c 223 mm = cm

f 495mm = cm

a 300 cm = m

d 900cm = m

b 500cm = m

e 2 000 cm = m

c 250cm = m

f 4550cm= m

a 1 000 mm = m

c 4500mm= m

b 5000mm= m

d 500mm = m



SERIES TOPIC

2 F 1

0 cm 51 6 102 7 113 8 12 14 154 9 13



Convert these lengths to centimetres:

Convert these lengths to millimetres:

Thisconversionboxcanhelpyou convertunitsoflength.

4

5

3

6

m mmcm

× 100

÷ 100

× 10

÷ 10

× 1 000

÷ 1 000

Units of length – m, cm, mm

To convert from mm to cm, divide by 10.

To convert from cm to mm, multiply by 10.

To convert from mm to m, divide by 1 000.

a 5cm = mm

d 7cm = mm

b 3 cm = mm

e 11 cm = mm

c 9cm = mm

f 15cm= mm

a 50mm = cm

d 15mm = cm

b 20 mm = cm

e 156mm = cm

c 223 mm = cm

f 495mm = cm

a 300 cm = m

d 900cm = m

b 500cm = m

e 2 000 cm = m

c 250cm = m

f 4550cm= m

a 1 000 mm = m

c 4500mm= m

b 5000mm= m

d 500mm = m

50

5

3

1

70

1.5

9

4.5

30

2

5

5

110

15.6

20

0.5

90

22.3

2.5

150

49.5

45.5



SERIES TOPIC

3F 1

Look carefully at how each shape is divided and find the missing length:

a

b

c

d

Units of length – find and order length

1

Don’t forget to check your answers match the units.

1 m

30 cm cm

3 m

150cm cm

200 cm

60cm cm

100 cm

30 cm 20 cmm

Convert all the lengths to the same unit.



SERIES TOPIC

3F 1

Look carefully at how each shape is divided and find the missing length:

a

b

c

d

Units of length – find and order length

1

Don’t forget to check your answers match the units.

1 m

30 cm cm

3 m

150cm cm

200 cm

60cm cm

100 cm

30 cm 20 cmm

Convert all the lengths to the same unit.

70

150

140

0.5



SERIES TOPIC

9F 2

a SunsetCovetoSandyBeach km

b MelodyPointtoSharkCliff km

c RecklessRockstoLagunaBeach km

d MelodyPointtoSandyBeachviaSharkCliff km

e LagunaBeachtoSharkCliffviaMelodyPoint km

Travelling far – measure distances

Write these distances in decimal notation:

Write these distances in metres:

Look carefully at Mermaid Island and work out how long these walking trails are. Record all answers in kilometres.

1

2

3

Shark Cliff

Sandy BeachSunset Cove

Reckless Rocks

Laguna Beach

Melody Point1245m

1572m

980m390m

415m712m

To convert from m to km, divide by 1 000.

a 2km123m = km

c 2km245m = km

e 8km145m = km

g 835m = km

b 4km235m = km

d 5km235m = km

f 8km23m = km

h 593m = km

a 3.6km = m

d 9.3km = m

g 5.6km = m

b 2.8km = m

e 8.2km = m

h 0.2km = m

c 0.6km = m

f 7.1km = m

i 0.1km = km



SERIES TOPIC

9F 2

a SunsetCovetoSandyBeach km

b MelodyPointtoSharkCliff km

c RecklessRockstoLagunaBeach km

d MelodyPointtoSandyBeachviaSharkCliff km

e LagunaBeachtoSharkCliffviaMelodyPoint km


Write these distances in decimal notation:

Write these distances in metres:

Look carefully at Mermaid Island and work out how long these walking trails are. Record all answers in kilometres.

1

2

3

Shark Cliff

Sandy BeachSunset Cove

Reckless Rocks

Laguna Beach

Melody Point1245m

1572m

980m390m

415m712m

To convert from m to km, divide by 1 000.

a 2km123m = km

c 2km245m = km

e 8km145m = km

g 835m = km

b 4km235m = km

d 5km235m = km

f 8km23m = km

h 593m = km

a 3.6km = m

d 9.3km = m

g 5.6km = m

b 2.8km = m

e 8.2km = m

h 0.2km = m

c 0.6km = m

f 7.1km = m

i 0.1km = km

2.123

2.245

8.145

0.835

4.235

5.235

8.023

0.593

3 600

9 300

5 600

2 800

8 200

200

600

7 100

100

0.98

1.572

0.712

1.962

2.817



SERIES TOPIC

10 F 2

Roadmapssometimeshavethedistancebetweentownswrittenontheroadthatconnectsthem.Thisinformationhelpsyouplanyourjourney.


Here is a page from Hannah’s journal where she has noted the places she went to during a road trip with her family. Add the distances that they travelled each day.

What is the total distance that Hannah and her family travelled? Show all of your working below. km

4

5

Scarborough

Lexia

96 km

285 km142 km520 km

340 km

218 km336 km

Brighton

MullalooHastings

Doubleview Woodvale Embleton

Day 1TodaywelefthomeatDoubleviewanddrovestraighttoHastings. km

Day 2WeleftHastingsafterbreakfastthenwehadlunchinMullaloo.Westayed thenightinBrighton. km

Day 3WedrovetoEmbletontofindoutaboutgettinganewpuppy! km

Day 4WehadtoleaveearlythismorningasitturnsoutthepuppywewantisinLexia. km

Day 5Ournewpuppyisagirl!WenamedherLexie,afterthetownshecamefrom. WedecidedtotraveluptoScarboroughtoshowLexietoourcousins. km

Day 6TodaywedroveallthewayfromScarboroughtoWoodvale.Dadwantedto keepgoingtillwegothomebutmummadehimstop. km

Day 7Todaywedrovetherestofthewayhome. km

420 km



SERIES TOPIC

10 F 2

Roadmapssometimeshavethedistancebetweentownswrittenontheroadthatconnectsthem.Thisinformationhelpsyouplanyourjourney.


Here is a page from Hannah’s journal where she has noted the places she went to during a road trip with her family. Add the distances that they travelled each day.

What is the total distance that Hannah and her family travelled? Show all of your working below. km

4

5

Scarborough

Lexia

96 km

285 km142 km520 km

340 km

218 km336 km

Brighton

MullalooHastings

Doubleview Woodvale Embleton

Day 1TodaywelefthomeatDoubleviewanddrovestraighttoHastings. km

Day 2WeleftHastingsafterbreakfastthenwehadlunchinMullaloo.Westayed thenightinBrighton. km

Day 3WedrovetoEmbletontofindoutaboutgettinganewpuppy! km

Day 4WehadtoleaveearlythismorningasitturnsoutthepuppywewantisinLexia. km

Day 5Ournewpuppyisagirl!WenamedherLexie,afterthetownshecamefrom. WedecidedtotraveluptoScarboroughtoshowLexietoourcousins. km

Day 6TodaywedroveallthewayfromScarboroughtoWoodvale.Dadwantedto keepgoingtillwegothomebutmummadehimstop. km

Day 7Todaywedrovetherestofthewayhome. km

420 km

340

662

336

621

96

935

420

3 410



SERIES TOPIC

17F 3

d

P = cm

e

P = cm

a

P = cm

b

P = cm

c

P = cm

Draw the following shapes and work out their perimeters:

c Arectanglethatistwiceaslongasitiswide.

P =

Perimeteristhelengtharoundtheoutsideofashape.

Perimeter – perimeter of shapes

Theperimeterofthesquareis8cm. Theperimeteroftherectangleis10cm.

These shapes are not to scale, so you can’t use your ruler to work out the perimeter. Can you find the perimeter of these shapes?

1

2

2 cm

2 cm

2 cm 2 cm

3 cm

3 cm

2 cm 2 cm

7cm

2 cm1 cm

5cm

7cm

1 cm

6cm

8 cm

9cm

9cm

a Asquarewith3cmsides.

P = cm

b Arectanglewithtwo4cmsidesand two3cmsides.

P = cm



SERIES TOPIC

17F 3

d

P = cm

e

P = cm

a

P = cm

b

P = cm

c

P = cm

Draw the following shapes and work out their perimeters:

c Arectanglethatistwiceaslongasitiswide.

P =

Perimeteristhelengtharoundtheoutsideofashape.


Theperimeterofthesquareis8cm. Theperimeteroftherectangleis10cm.

These shapes are not to scale, so you can’t use your ruler to work out the perimeter. Can you find the perimeter of these shapes?

1

2

2 cm

2 cm

2 cm 2 cm

3 cm

3 cm

2 cm 2 cm

7cm

2 cm1 cm

5cm

7cm

1 cm

6cm

8 cm

9cm

9cm

a Asquarewith3cmsides.

P = cm

b Arectanglewithtwo4cmsidesand two3cmsides.

P = cm

Teacher check.

18

12 14

16 12

3628



SERIES TOPIC

18 F 3

a

d

b

e

c

6cm 4cm

4cm3 cm5cm

Find the perimeter of these regular polygons*:

The perimeters of some regular polygons are given in the table below. Fill in the length of the sides:

Theseregularpolygons*havesidesofequallengths.


3

4

Perimeter 24cm 40cm 48cm 25cm

Length of each side

*Not drawn to scale.

2 cmP = 16 cm

2 cmP = 10 cm

1 cmP = 6 cm

1 cmP = 4 cm

What is the fastest way to do this?

P = cm

P = cm

P = cm

P = cm

P = cm



SERIES TOPIC

18 F 3

a

d

b

e

c

6cm 4cm

4cm3 cm5cm

Find the perimeter of these regular polygons*:

The perimeters of some regular polygons are given in the table below. Fill in the length of the sides:

Theseregularpolygons*havesidesofequallengths.


3

4

Perimeter 24cm 40cm 48cm 25cm

Length of each side


2 cmP = 16 cm

2 cmP = 10 cm

1 cmP = 6 cm

1 cmP = 4 cm

What is the fastest way to do this?

P = cm

P = cm

P = cm

P = cm

P = cm20

30 32

18 16

4 cm 10 cm 6 cm 5 cm



SERIES TOPIC

19F 3

a

b

c

e

g

d

f

h

Perimeter – calculate perimeter

Find the perimeter of these shapes. Choose a unit of measurement to express your answer.1

20 cm

2 m

40cm

45cm

1.5m

1.8 m

7m2 m

6m

These shapes are all symmetrical. How does that help me?

P =

P =

P =

1.5m

20 cm

P =

3 m

8 m

P =

9m 1 m 3 m

2 m

P =

P =

P =



SERIES TOPIC

19F 3

a

b

c

e

g

d

f

h


Find the perimeter of these shapes. Choose a unit of measurement to express your answer.1

20 cm

2 m

40cm

45cm

1.5m

1.8 m

7m2 m

6m

These shapes are all symmetrical. How does that help me?

P =

P =

P =

1.5m

20 cm

P =

3 m

8 m

P =

9m 1 m 3 m

2 m

P =

P =

P =

170 cm

440 cm

6.6 m

22 m

48 m

28 m

56 m

3.4 m



SERIES TOPIC

20 F 3

a b

c

Irregularshapesarenotsymmetrical.Thismeansweneedtomeasureeachside.

2

3

Why? __________________________________________________________________________________

_______________________________________________________________________________________

4m

3 m

6m

14m

9m

Pool A4m

4m

10 m

6m

6m

3 m

Pool B


P = cm

P = cm

6cm

3 cm

3 cm

1 cm

1 cm

1 cm

1 cm

2 cm

2 cm

4cm

Find the perimeters of these irregular shapes:

P = cm

1 cm

3 cm

4cm

2 cm

2 cm

3 cm

3 cm

2 cm

Which of these designs for backyard pools would be the least expensive to fence?

1 cm

1 cm

2 cm

1 cm

3 cm

4cm

3 cm

5cm



SERIES TOPIC

20 F 3

a b

c

Irregularshapesarenotsymmetrical.Thismeansweneedtomeasureeachside.

2

3

Why? __________________________________________________________________________________

_______________________________________________________________________________________

4m

3 m

6m

14m

9m

Pool A4m

4m

10 m

6m

6m

3 m

Pool B


P = cm

P = cm

6cm

3 cm

3 cm

1 cm

1 cm

1 cm

1 cm

2 cm

2 cm

4cm

Find the perimeters of these irregular shapes:

P = cm

1 cm

3 cm

4cm

2 cm

2 cm

3 cm

3 cm

2 cm

Which of these designs for backyard pools would be the least expensive to fence?

1 cm

1 cm

2 cm

1 cm

3 cm

4cm

3 cm

5cm

24

20

20

Pool B

The perimeter of Pool B is smaller than the perimeter of Pool A.

Pool A = 36 m Pool B = 33 m



SERIES TOPIC

23F 3

What to do

Perimeter problems solve

a Thelengthofarectangleisdoubleitswidth.Findtheperimeterifthewidth is 200 cm.

b Thelengthofarectangleis6timesitswidth.Findthelengthandwidthoftherectangleiftheperimeteris7metres.

c Charlieranaroundtheschool3times.Howfardidsherun?Writeyouranswer inkm.

d Jakewantstobuildafencearoundhisswimmingpooltocomplywithsafetyregulations.Ifthelengthofhispoolareais6metresandthewidthis4metres,howmuchwillitcost?Fencingcosts$55.50ametre.

100 m

280 m

200 m

40m

300 m



SERIES TOPIC

23F 3

What to do

Perimeter problems solve

a Thelengthofarectangleisdoubleitswidth.Findtheperimeterifthewidth is 200 cm.

b Thelengthofarectangleis6timesitswidth.Findthelengthandwidthoftherectangleiftheperimeteris7metres.

c Charlieranaroundtheschool3times.Howfardidsherun?Writeyouranswer inkm.

d Jakewantstobuildafencearoundhisswimmingpooltocomplywithsafetyregulations.Ifthelengthofhispoolareais6metresandthewidthis4metres,howmuchwillitcost?Fencingcosts$55.50ametre.

100 m

280 m

200 m

40m

300 m

1 200 cm or 12 m

Length = 3 m

Width = 50 cm

1 160 m × 3 = 3.48 km

20 × $55.50 = $1 110



SERIES TOPIC

25F 4

a

Area= cm2

b

Area= cm2

c

Area= cm2

What is the area of each rectangle? Each square in the grid has an area of 1 cm². Some of the squares have been marked in for you.

d Didyouneedtoseeallthesquarestoworkoutthearea?__________

What is the area of each shaded shape? Each square in the grid has an area of 1 cm².

Shade the grid to show a rectangle with the area of 6 cm².

Area – introducing area

1

2

3

Areaistheamountofspaceashapecovers.Itisa2Dmeasurement.

Wemeasureareainsquareunits.Forsmallareasweusesquarecentimetres. 1 cm

1 cm

a

Area= cm2

b

Area= cm2

c

Area= cm2



SERIES TOPIC

25F 4

a

Area= cm2

b

Area= cm2

c

Area= cm2

What is the area of each rectangle? Each square in the grid has an area of 1 cm². Some of the squares have been marked in for you.

d Didyouneedtoseeallthesquarestoworkoutthearea?__________

What is the area of each shaded shape? Each square in the grid has an area of 1 cm².

Shade the grid to show a rectangle with the area of 6 cm².


1

2

3

Areaistheamountofspaceashapecovers.Itisa2Dmeasurement.

Wemeasureareainsquareunits.Forsmallareasweusesquarecentimetres. 1 cm

1 cm

a

Area= cm2

b

Area= cm2

c

Area= cm2

4

15 20 18

2 4

Answers will vary.

3 × 2 rectangle shaded.Sample answer.

No



SERIES TOPIC

26 F 4

In each shape*, you are given the area but one side is not labelled. Label the missing side:

Find the areas of these shapes*:

Wecanusethisformulatofindtheareaofrectangles:

Area=length×width

Area=3×5=15cm2

a b c

d e f

a b c

6cm

4cm

2 cm

5cm

2 cm

3 cm

8 m

4m

4cm

4cm

1 cm

4cm

5cm

5cm

3 cm 3 cm

4

5



Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= m2

Area= cm2

Area=20m2

4m

Area=14m2

7mArea=24m2

8 m



SERIES TOPIC

26 F 4

In each shape*, you are given the area but one side is not labelled. Label the missing side:

Find the areas of these shapes*:

Wecanusethisformulatofindtheareaofrectangles:

Area=length×width

Area=3×5=15cm2

a b c

d e f

a b c

6cm

4cm

2 cm

5cm

2 cm

3 cm

8 m

4m

4cm

4cm

1 cm

4cm

5cm

5cm

3 cm 3 cm

4

5



Area= cm2

Area= cm2

Area= cm2

Area= cm2

Area= m2

Area= cm2

Area=20m2

4m

Area=14m2

7mArea=24m2

8 m

24

10 32 6

16 4

5 m

2 m

3 m



SERIES TOPIC

28 F 4

Order the states and territories from smallest to largest areas:

Find the area of each large area*. Write your answer in hectares.

Hectaresareusedtomeasurelargespacessuchasafootballfield.

Wewritehectaresasha.Onehectareisequalto10000m².

Anevenlargerunitisasquarekilometrekm².Onesquarekilometreisequalto100hectares.

1ha=10000m² 1km²=1000000m²

Area – hectares and square kilometres

1

2

1 _________________________

4 _________________________

7 _________________________

2 _________________________

5 _________________________

8 _________________________

3 _________________________

6 _________________________

a

Area= hectares

b

Area= hectares

c

Area= hectares

300 m

100 m250m

100 m

120 m

120 m

d

Area= hectares

e

Area= hectares

f

Area= hectares

100 m

450m

200 m

300 m400m

150m

States and Territories Area

Queensland 1727200km²

New South Wales 801600km²

Victoria 227600km²

ACT 2400km²

WesternAustralia 2525500km²

SouthAustralia 984000km²

Tasmania 67800km²

NorthernTerritory 1346200km²

1km²=1000000m²

WESTERNAUSTRALIA

NORTHERNTERRITORY

QUEENSLAND

NEWSOUTHWALES

SOUTH AUSTRALIA

TASMANIA




SERIES TOPIC

28 F 4

Order the states and territories from smallest to largest areas:

Find the area of each large area*. Write your answer in hectares.

Hectaresareusedtomeasurelargespacessuchasafootballfield.

Wewritehectaresasha.Onehectareisequalto10000m².

Anevenlargerunitisasquarekilometrekm².Onesquarekilometreisequalto100hectares.

1ha=10000m² 1km²=1000000m²

Area – hectares and square kilometres

1

2

1 _________________________

4 _________________________

7 _________________________

2 _________________________

5 _________________________

8 _________________________

3 _________________________

6 _________________________

a

Area= hectares

b

Area= hectares

c

Area= hectares

300 m

100 m250m

100 m

120 m

120 m

d

Area= hectares

e

Area= hectares

f

Area= hectares

100 m

450m

200 m

300 m400m

150m

States and Territories Area

Queensland 1727200km²

New South Wales 801600km²

Victoria 227600km²

ACT 2400km²

WesternAustralia 2525500km²

SouthAustralia 984000km²

Tasmania 67800km²

NorthernTerritory 1346200km²

1km²=1000000m²

WESTERNAUSTRALIA

NORTHERNTERRITORY

QUEENSLAND

NEWSOUTHWALES

SOUTH AUSTRALIA

TASMANIA


3

6 4.5 6

2.5 1.44

ACT

New South Wales

Queensland

Tasmania

South Australia

Western Australia

Victoria

Northern Territory



SERIES TOPIC

29F 4

Use the 1 cm grid below to draw three shapes with areas of 10 cm² but with different perimeters. Record the perimeter of each shape:

Use the grid below to draw two shapes with a perimeter of 12 cm but with different areas:

Area – area and perimeter

Find the perimeter and area of each shape:1

2

3

a b

c d

P = __________

A=__________

P = __________

A=__________

P = __________

A=__________P = __________

A=__________

a P = cm b P = cm c P = cm

1 cm

1 cm

1 cm

1 cm



SERIES TOPIC

29F 4

Use the 1 cm grid below to draw three shapes with areas of 10 cm² but with different perimeters. Record the perimeter of each shape:

Use the grid below to draw two shapes with a perimeter of 12 cm but with different areas:


Find the perimeter and area of each shape:1

2

3

a b

c d

P = __________

A=__________

P = __________

A=__________

P = __________

A=__________P = __________

A=__________

a P = cm b P = cm c P = cm

1 cm

1 cm

1 cm

1 cm

Answers will vary.

Answers will vary.

16 cm

14 cm

12 cm

20 cm

16 cm²

12 cm²

9 cm²

16 cm²



SERIES TOPIC

30 F 4

Draw 3 different rectangles that have a perimeter of 24 cm and record the area in the table. The first row in the table is a hint of where to start.

Draw as many different rectangles as you can with the area of 36 cm². Label the length of each side:

4

5

Length Width Area

10 2




SERIES TOPIC

30 F 4

Draw 3 different rectangles that have a perimeter of 24 cm and record the area in the table. The first row in the table is a hint of where to start.

Draw as many different rectangles as you can with the area of 36 cm². Label the length of each side:

4

5

Length Width Area

10 2


Teacher check.

Teacher check.



SERIES TOPIC

32 F 4

d

Area= cm2

e

Area= cm2

f

Area= cm2

a

Area= cm2

b

Area= cm2

c

Area= cm2

What to do next

Drawacompositeshapethathasanareaof50cm².

What to do

Composite calculations apply

Canyoufindtheareasoftheserooms*?Circletheroomthatwouldbecheapest tocarpet.

Putacrossintheroomthatwouldbemostexpensive.

4cm

9cm

12 cm

6cm

8 cm

8 cm

5cm

5cm

3 cm

2 cm

8 cm

1 cm2 cm

6cm6cm

9cm

6cm

3 cm

3 cm

9cm


15cm8 cm

7cm

3 cm

11 cm

4cm3 cm

2 cm3 cm



SERIES TOPIC

32 F 4

d

Area= cm2

e

Area= cm2

f

Area= cm2

a

Area= cm2

b

Area= cm2

c

Area= cm2

What to do next

Drawacompositeshapethathasanareaof50cm².

What to do

Composite calculations apply

Canyoufindtheareasoftheserooms*?Circletheroomthatwouldbecheapest tocarpet.

Putacrossintheroomthatwouldbemostexpensive.

4cm

9cm

12 cm

6cm

8 cm

8 cm

5cm

5cm

3 cm

2 cm

8 cm

1 cm2 cm

6cm6cm

9cm

6cm

3 cm

3 cm

9cm


15cm8 cm

7cm

3 cm

11 cm

4cm3 cm

2 cm3 cm

Teacher check.

50

50 84 101

18 63

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