Map Scale (S3-NT)
Scale of Drawing = Drawing length : Actual length
Map Scale = Map distance : Actual Distance
If the scale of a map is given as 1 : 200 000
=> 1cm represents 200 000 cm (200 000 cm = 2000m = 2km)
=> 1cm represents 2 km
1cm : 2km
1cm x 1cm = 1cm2: 2km x 2 km = 4km2
1cm2: 4 km2
* Area calculation: (first calculate 1cm2 represent how many km2)
Example
The scale of a map is given as 1 : 200 000
Scale representation and conversion
a. Complete the following
Scale of map is 1cm to km
Step 1: Write the conversion
1km = 100 x 1000
= 100 000 cm
Step 2: Find the conversion scale
Divide given scale by conversion
200 000 / 1001000 = 2km
Step 3: Solve
Scale of map is 1cm to 2 km
To Find Distance on the map ( Given actual distance)
b. Find the distance on the map between two towns that are actually 30 km apart.
Step1: Write the scale
1 cm : 2 km [[ MUST write this scale FIRST when doing ALL questions ]]
Step2: ‘line’ the number and compute
1cm : 2km
? : 30km
30 km apart is 30/2 = 15 cm on map
Distance on the map is 15 cm.
To find Actual Distance (Given distance on the map)
c. Find the actual distance of two towns are that 10 cm apart on the map.
Working:
1 cm : 2 km
10 cm = 10 x 2 = 20
Actual distance = 20 km
To Find Actual Area (Given area of map)
d. A forest has an area of 5 cm2 on the map. Find the actual area of the forest in square kilometres.
Step 1: Write the scale and compute to area mapping
1 cm : 2 km
1cm2 => 2km x 2km = 4 km2
Step 2: ‘line’ the number and compute (multiply to find actual value)
1cm2 : 4 km2
5 cm2 : ?
5cm2 => 4 x 5 = 20
Actual area of forest = 20 km2
To find Area on Map (Given actual area)
e. The actual area of a town is 120 km2. What is the area on the map?
Step 1: Write the scale and compute to area mapping
1 cm : 2 km
1cm2 => 2km x 2km = 4 km2
Step 2: ‘line’ the number and compute (divide to find map value)
1cm2 : 4 km2
? : 120 km2
120 km2 => 120 / 4 = 30cm2
Area of town on map is 30cm2
Practice
1. Write 480 : 400 in its simplest form.
2. The scale of the map in given as 1cm : 2 km
a. Scale of the map is 1 : ___________
b. The distance between two towns is 30km. What is this distance, in cm on the map?
c. A forest has an area of 8cm2 on the map. What is the actual area of the forest in km2.
3a. Write 50 000 cm in kilometres.
A map is drawn to a scale of 1 : 50 000
b. The distance between two stations on the map is 12cm
Find the real distance between the stations in kilometres
c. The distance between two towns is 35 km. How far is this distance on the map?
