1. Using the Scale of a Map
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2. What is the direct air distance from London to Athens?
17.6 cm x = cm = m
= 3 432 km
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3. What is the direct air distance from London to Budapest?
10.5 cm x = cm = m
≈ 2 048 km
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4. What is the true distance for every mm on this map?x = mm = m
= 19.5 km
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5. What is the direct air distance from London to Warsaw?
3.5 cm
= 300 miles
x 3.03
x 3.03
10.6 cm
= ? miles
909
10.6
÷ 3.5
≈ 3.03
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6. What is the direct air distance from London to Berlin?
3.5 cm
= 300 miles
x 1.97
x 1.97
6.9 cm
= ? miles
591
6.9
÷ 3.5
≈ 1.97
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7. Another Example
Scale 1 :
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8. Find the distance between the 2 points on this map
Scale 1 :
6.8 cm x = cm
= 8 500 m
= 8.5 km
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9. 20 km
Another Example
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10. Find the distance between the 2 points marked on this map
20 km
5.3 cm
= 20 km
x 2.15
x 2.15
11.4 cm
= ? km 43
11.4
÷ 5.3
≈ 2.15
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11. Floor
Plans
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12. 3.328 m
The diagram opposite shows an architect’s floor plan for a bathroom.
The scale of this plan is 1 : 32
Calculate the internal width and length of this bathroom and the width of the door [in m]
door
10.4 cm
x 32
= 332.8 cm
= 3.328 m
© T Madas

13. 3.328 m
The diagram opposite shows an architect’s floor plan for a bathroom.
The scale of this plan is 1 : 32
Calculate the internal width and length of this bathroom and the width of the door [in m]
door
3.168 m
10.4 cm
x 32
= 332.8 cm
= 3.328 m
9.9 cm
x 32
= 316.8 cm
= 3.168 m
© T Madas

14. 3.328 m
The diagram opposite shows an architect’s floor plan for a bathroom.
The scale of this plan is 1 : 32
Calculate the internal width and length of this bathroom and the width of the door [in m]
door
3.168 m
10.4 cm
x 32
= 332.8 cm
= 3.328 m
9.9 cm
x 32
= 316.8 cm
= 3.168 m
2.5 cm
x 32
= 80 cm
= 0.8 m
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15. Another Example
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16. The diagram opposite shows an architect’s floor plan for an office, consisting of 2 rooms
The scale of this plan is 1 : 40
Calculate the internal dimensions of the two rooms in metres
Desk A
Desk B
9.4 cm
x 40
= 376 cm
= 3.76 m
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17. The diagram opposite shows an architect’s floor plan for an office, consisting of 2 rooms
The scale of this plan is 1 : 40
Calculate the internal dimensions of the two rooms in metres
Desk A
Desk B
9.4 cm
x 40
= 376 cm
= 3.76 m
7.1 cm
x 40
= 284 cm
= 2.84 m
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18. The diagram opposite shows an architect’s floor plan for an office, consisting of 2 rooms
The scale of this plan is 1 : 40
Calculate the internal dimensions of the two rooms in metres
Desk A
Desk B
3.76 m by 2.84 m
9.4 cm
x 40
= 376 cm
= 3.76 m
3.76 m by 3.28 m
7.1 cm
x 40
= 284 cm
= 2.84 m
8.2 cm
x 40
= 328 cm
= 3.28 m
© T Madas

19. © T Madas

20. Scale 1 : 20 : 13 cm 9 cm ? tallest average shortest
The average height of a human adult male is 180 cm and this is shown below using the scale 1 : 20
Using the same scale, the tallest and the shortest man in the world are also drawn for comparison.
1. What is the actual height of the tallest man in the world?
2. If the actual height of the shortest man in the world is 70 cm
what is his height in the drawing?
Scale 1 : 20
drawing 1
1 cm
13 cm :
actual 20
20 cm
260 cm
13 cm
x13
x13
9 cm ?
tallest
average
shortest
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21. Scale 1 : 20 : 13 cm 9 cm 3.5 cm 70 cm ? tallest average shortest
The average height of a human adult male is 180 cm and this is shown below using the scale 1 : 20
Using the same scale, the tallest and the shortest man in the world are also drawn for comparison.
1. What is the actual height of the tallest man in the world?
2. If the actual height of the shortest man in the world is 70 cm
what is his height in the drawing?
Scale 1 : 20
drawing 1
1 cm
2 cm
3 cm
4 cm :
actual 20
20 cm
40 cm
60 cm
80 cm
13 cm
9 cm
3.5 cm
70 cm ?
tallest
average
shortest
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22. © T Madas

23. A model of a helicopter is made to a scale of 2 cm to 1 m.
1. Calculate the actual span of the helicopter’s rotor in m,
if it measures 16 cm in the model.
2. What is the span of the tail rotor in the model in cm,
if its actual span is 2.5 m?
Model cm 2 16 :
Actual m 1 8
x 8
x 8
The rotor has an actual span of 8 m
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24. A model of a helicopter is made to a scale of 2 cm to 1 m.
1. Calculate the actual span of the helicopter’s rotor in m,
if it measures 16 cm in the model.
2. What is the span of the tail rotor in the model in cm,
if its actual span is 2.5 m?
Model cm 2 5 :
Actual m 1
2.5
x 2.5
x 2.5
The tail rotor has a span of 5 cm in the model
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25. © T Madas

26. 9 cm cm m The diagram opposite shows an architect’s plan for a bedroom
The scale of this plan is 1 : 36
Calculate the internal area of this bedroom in m2, correct to 2 d.p.
9 cm
x 36
= 324 cm
= 3.24 m
© T Madas

27. 3.24 m
The diagram opposite shows an architect’s plan for a bedroom
The scale of this plan is 1 : 36
Calculate the internal area of this bedroom in m2, correct to 2 d.p.
9 cm
x 36
= 324 cm
4.68 m
= 3.24 m
13 cm
x 36
= 468 cm
= 4.68 m
© T Madas

28. 3.24 m
The diagram opposite shows an architect’s plan for a bedroom
The scale of this plan is 1 : 36
Calculate the internal area of this bedroom in m2, correct to 2 d.p.
9 cm
x 36
= 324 cm
4.68 m
= 3.24 m
A = m2 (2 d.p.)
13 cm
x 36
= 468 cm
= 4.68 m
3.24
x 4.68 = m2
© T Madas

29. © T Madas

30. 1 cm = 1 : 200 m 20000 cm 20000 1 inch = 1.5 inch = 2.54 cm 3.81 cm
The scale of a town map is 1 cm = 200 m
On this map, the town hall is 1½ inches away from the local church.
1. Write down the scale of this map as a unit ratio, in the
form 1 : …
2. Calculate the distance between the town hall and the
local church, correct to the nearest 10 metres
1 cm =
1 :
200 m
20000 cm
20000
1 inch =
1.5 inch =
2.54 cm
3.81 cm
3.81 cm
x 20000
= 76200 cm
= 762 m
≈ 760 m
© T Madas

31. © T Madas

32. The length of a model helicopter is 40 cm.
The actual length of the helicopter is 18.4 m
1. Write down the scale of this model as a unit ratio, in the
form 1 : …
2. Calculate the actual span of the helicopter’s rotor in m,
if it measures 35 cm in the model.
3. What is the span of the tail rotor in the model in cm,
if its actual span is 2.07 m?
40 cm =
1 :
18.4 m
1840 cm 46
35 cm
x 46
= 1610 cm
= 16.1 m
2.07 m
÷ 46
= 0.045 m
= 4.5 cm
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33. © T Madas