Scale and maps
Use scale factors and map scales to convert between map measurements and real-life distances and areas.
Worked examples
Finding the real distance from a map measurement
Straightforward
Problem
A map has a scale of . A road measures cm on the map. Find the real length of the road in kilometres.
1
Interpret the scale.
A scale of means cm on the map represents cm in real life.
2
Multiply the map distance by the scale factor.
cm
3
Convert centimetres to kilometres.
km
Answer
The real length of the road is km.
Finding the map distance from a real distance
Moderate
Problem
A map has a scale of . The real distance between two lakes is km. Find the distance between the lakes on the map in centimetres.
1
Convert the real distance to centimetres.
km cm
2
Divide by the scale factor to find the map distance.
cm
3
Check by working backwards.
cm km ✓
Answer
The distance on the map is cm.
Finding the real area from a scale drawing
Challenging
Problem
A plan has a scale of . A rectangular garden on the plan measures cm by cm. Find the real area of the garden in square metres.
1
Find the real length of each side in centimetres.
Length: cm \\ Width: cm
2
Convert each dimension to metres.
Length: m \\ Width: m
3
Calculate the real area.
m²
4
Alternative method: use the area scale factor.
Area scale factor \\ Plan area cm² \\ Real area cm² m²
Answer
The real area of the garden is m².
Practise
Q1·Straightforward
A map has a scale of . A road measures cm on the map. Find the real length of the road in kilometres.
Explanation
Real distance in cm: cm. Convert to km: km.
Q2·Straightforward
A map has a scale of . A path measures cm on the map. Find the real length of the path in kilometres.
Explanation
Real distance in cm: cm. Convert to km: km.
Q3·Straightforward
A floor plan has a scale of . A wall measures cm on the plan. Find the real length of the wall in metres.
Explanation
Real length in cm: cm. Convert to metres: m.
Q4·Straightforward
A scale drawing has a scale of . A room measures cm on the drawing. Find the real length of the room in metres.
Explanation
Real length in cm: cm. Convert to metres: m.
Q5·Moderate
A map has a scale of . Two towns are km apart in real life. Find the distance between the towns on the map in centimetres.
Explanation
Convert real distance: km cm. Map distance: cm.
Q6·Moderate
A map has a scale of . The real distance between two landmarks is km. Find the distance between them on the map in centimetres.
Explanation
Convert real distance: km cm. Map distance: cm.
Q7·Moderate
A scale drawing of a building uses a scale of . A wall segment measures cm on the drawing. Find the real length of the wall in metres.
Explanation
Real length in cm: cm. Convert to metres: m.
Q8·Moderate
A map has a scale of . Two cities are cm apart on the map. Find the real distance between the cities in kilometres.
Explanation
Real distance in cm: cm. Convert to km: km.
Q9·Challenging
On a map, two towns appear cm apart. The actual distance between the towns is km. The map scale is written as . Find the value of .
Explanation
Convert real distance: km cm. Scale factor: . The scale is .
Q10·Challenging
A map shows two points cm apart. The real distance between them is km. The map scale is written as . Find the value of .
Explanation
Convert real distance: km cm. Scale factor: . The scale is .
Q11·Challenging
A scale drawing of a park uses a scale of . On the drawing, the park covers an area of cm². Find the real area of the park in square metres.
Explanation
The scale factor for lengths is , so the scale factor for areas is . Real area in cm²: cm². Convert to m²: m².
Q12·Challenging
A plan uses a scale of . A block of land has an area of cm² on the plan. Find the real area of the block in square metres.
Explanation
Area scale factor: . Real area in cm²: cm². Convert to m²: m².