This presentation shows worked examples on the topic.

1. SCALES AND
SCALE
DRAWINGS

2. VOCABULARY
2
Scale Drawing
A SCALE DRAWING is a proportional
two-dimensional drawing of an
object.
Scale Factor
The SCALE FACTOR is a ratio of the
dimensions of the drawing to the
dimensions of the actual object.

3. VOCABULARY
3
Scale Model
A SCALE MODEL is a proportional
three-dimensional model of an
object.
Scale
A SCALE is the ratio of two sets of
measurements.

4. 4
 In a blueprint, the length and width of a building
which measures 144 m x 108 m are shown to be 18
cm and 13.5 cm respectively.
What is the scale factor used for the blueprint?
Write a ratio using one of the dimensions, then simplify:
𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 =
𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑛 𝑏𝑙𝑢𝑒𝑝𝑟𝑖𝑛𝑡
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
=
18
144
𝒔𝒄𝒂𝒍𝒆 𝒇𝒂𝒄𝒕𝒐𝒓 =
𝟏
𝟖
EXAMPLE 1
Finding a scale factor

5. 5
 The table shows the dimensions of a plane model
and its blueprint.Calculate the scale factor.
Write a ratio using one of the dimensions, then simplify:
𝑠𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 =
6
36
=
𝟏
𝟔
EXAMPLE 2
Finding a scale factor
Model Blueprint
Length (cm) 24 4
Wingspan (cm) 36 6

6. 6
A portrait was enlarged to be placed on a wall in
Alicia’s living room.The enlarged portrait has
dimensions 80 cm x 45 cm. If the scale factor is 1:5.
What are the dimensions of the original portrait?
𝑆𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 =
𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛
𝑒𝑛𝑙𝑎𝑟𝑔𝑒𝑑 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛
𝐿𝑒𝑡 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ 𝑏𝑒 𝑙.
1
5
=
𝑙
80
𝑙 =
80
5
= 𝟏𝟔 𝒄𝒎
𝐿𝑒𝑡 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑤𝑖𝑑𝑡ℎ 𝑏𝑒 𝑤.
1
5
=
𝑤
45
𝑤 =
45
5
= 𝟗 𝒄𝒎
EXAMPLE 3
Finding unknown length given the scale factor.

7. 7
The distance between Arima and Port-of-Spain is 26 km. If a map is drawn using a scale which is 1
cm : 4 km, what is the distance between the two cities on the map?
𝑆𝑐𝑎𝑙𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 =
𝑚𝑎𝑝 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒
𝐿𝑒𝑡 𝑡ℎ𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑝 𝑏𝑒 𝑑.
𝑑
26
=
1
4
𝑑 =
26
4
= 𝟔. 𝟓 𝒄𝒎
𝑇ℎ𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝐴𝑟𝑖𝑚𝑎 𝑎𝑛𝑑 𝑃𝑜𝑟𝑡 − 𝑜𝑓 − 𝑆𝑝𝑎𝑖𝑛 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑝 𝑖𝑠 𝟔. 𝟓 𝒄𝒎.
EXAMPLE 4

8. EXAMPLE 5
The scale of a sketch map ofTrinidad is 1:500 000. Determine the actual distance in
centimetres between:
Port-of-Spain andTacarigua if the distance on the map is 2.8 cm.
𝐿𝑒𝑡 𝑡ℎ𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒 𝑥.
1𝑐𝑚 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 500 000 𝑐𝑚
2.8 𝑐𝑚 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 500 000 × 2.8 = 1 400 000 𝑐𝑚
𝒙 = 𝟏 𝟒𝟎𝟎 𝟎𝟎𝟎 𝒄𝒎
8

9. EXAMPLE 6
The scale of a sketch map ofTrinidad is 1:500 000. Determine the actual distance
in kilometres between:
Port-of-Spain and Guayaguayare if the distance on the map is 15.3 cm.
𝐿𝑒𝑡 𝑡ℎ𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒 𝑥.
1𝑐𝑚 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 500 000 𝑐𝑚
15.3 𝑐𝑚 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 15.3 × 500 000 = 7 650 000 𝑐𝑚
𝒙 =
𝟕 𝟔𝟓𝟎 𝟎𝟎𝟎
𝟏𝟎𝟎 𝟎𝟎𝟎
= 𝟕𝟔. 𝟓 𝒌𝒎
9

10. EXAMPLE 7
• The area of a cricket pitch is 90 𝑚2. On a map, the area is 0.9 𝑐𝑚2.
a) What is the area of the actual pitch in centimetres squared?
1 𝑚2
= 100 × 100 = 10 000 𝑐𝑚2
90 𝑚2
= 90 × 10 000 𝑐𝑚2
= 𝟗𝟎𝟎 𝟎𝟎𝟎 𝒄𝒎𝟐
b) Calculate the ratio of the areas given.
𝑚𝑎𝑝 𝑎𝑟𝑒𝑎: 𝑎𝑐𝑡𝑢𝑎𝑙 𝑎𝑟𝑒𝑎 = 0.9 ∶ 900 000
When we simplify, we get
𝟎.𝟗
𝟎.𝟗
:
𝟗𝟎𝟎 𝟎𝟎𝟎
𝟎.𝟗
= 𝟏: 𝟏 𝟎𝟎𝟎 𝟎𝟎𝟎
10

11. EXAMPLE 7 continued
• The area of a cricket pitch is 90 𝑚2
. On a map, the area is 0.9 𝑐𝑚2
.
a) The actual area of the pitch is
𝟗𝟎𝟎 𝟎𝟎𝟎 𝒄𝒎𝟐
b) The ratio of the areas is
𝟏: 𝟏 𝟎𝟎𝟎 𝟎𝟎𝟎
c) Determine the scale of the map
𝑡ℎ𝑒 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑎 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑛 𝑡ℎ𝑒 𝑚𝑎𝑝 𝑡𝑜 𝑡ℎ𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝑠𝑞𝑢𝑎𝑟𝑒 𝑟𝑜𝑜𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑟𝑒𝑎𝑠
1: 1 000 000 = 1: 1000
𝑻𝒉𝒆 𝒔𝒄𝒂𝒍𝒆 𝒊𝒔 𝟏: 𝟏𝟎𝟎𝟎
11

12. 12
1
40
=
𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛 𝑖𝑛 𝑑𝑟𝑎𝑤𝑖𝑛𝑔
𝑎𝑐𝑡𝑢𝑎𝑙 𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛
1
40
=
9
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ
𝑎𝑛𝑑
1
40
=
6
𝑎𝑐𝑡𝑢𝑎𝑙 𝑤𝑖𝑑𝑡ℎ
𝑎𝑐𝑡𝑢𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ = 9 × 40 = 360 𝑐𝑚
𝑎𝑐𝑡𝑢𝑎𝑙 𝑤𝑖𝑑𝑡ℎ = 6 × 40 = 240 𝑐𝑚
𝐴𝑐𝑡𝑢𝑎𝑙 𝑎𝑟𝑒𝑎 = 360 × 240 = 𝟖𝟔 𝟒𝟎𝟎 𝒄𝒎𝟐
EXAMPLE 8
A scale of 1:40 was used to make a scale drawing
of a rectangular room.The dimensions of the
room in the drawing are 9 cm by 6 cm.What is
the actual area of the room in 𝑐𝑚2
?

13. TRYTHIS
An island is drawn on a grid of 1 cm squares and drawn to a scale of 1:50 000. Fill in
the blanks.
a) 1 cm on the map represents ______ cm on the island.
b) An area of 1 𝑐𝑚2
on the map represents an area of
_______ 𝑐𝑚2 on the island.
c) Given that 1 km = 100 000 cm. 1 cm on the map
represents ______ km on the island.
d) The distance from L to M on the map is ______ cm.
e) The actual distance from L to M is _______ km. 13

14. SOLUTIONS
An island is drawn on a grid of 1 cm squares and drawn to a scale of 1:50 000. Fill in
the blanks.
a) 1 cm on the map represents _50 000 cm on the island.
b) An area of 1 𝑐𝑚2
on the map represents an area of 2
500 000 000 𝒄𝒎𝟐
on the island.
c) Given that 1 km = 100 000 cm. 1 cm on the map
represents 0.5 km on the island.
d) The distance from L to M on the map is 8 cm.
e) The actual distance from L to M is 4 km. 14

15. THE
END!