Why square the scale for area?

Both length and width shrink by the scale, so the area shrinks by its square.

When use four or six figures?

Four figures locate a place roughly, while six pin it down to a hundred metres.

Primary General Studies, Maps and Directions, Paper 4: area scale, back bearings and measuring routes

2026-10-31

Tutor Prep Guide · Primary General Studies

Ten items on the area of a rectangle on a 1:25,000 map, adding 180 degrees for a back bearing, converting 600 m to map centimetres, four and six figure precision, squared scale for areas, a 5 km road, three map types, measuring winding routes, latitude and longitude.

Focus　Convert each side then multiply, so 4 cm and 3 cm at 1:25,000 give 1,000 m by 750 m or 0.75 km²; a back bearing adds 180 degrees, so 060 becomes 240; metres become centimetres after multiplying by 100 then dividing by the scale, giving 3 cm; six figures are accurate to 100 m and four to 1 km; area ratios are the square of the scale, here 4 times; winding routes need string or short sections; 22 degrees north and 114 degrees east place Hong Kong in the northern and eastern hemispheres; an area never scales by one factor of the scale only.

01　Paper details (check answers afterwards)

Item	Detail
Questions	10
Suggested time	25
Difficulty mix	Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1
Chapter	Chapter: Primary General Studies: Maps and Directions
Level	P4 to P6

02　Questions (10 items)

FoundationOn a 1:25,000 map a rectangle measures 4 cm by 3 cm. What are the real sides in metres and the area in square kilometres?
FoundationThe bearing from A to B is 060 degrees. What is the bearing from B back to A?
FoundationTwo places are 600 m apart. How many centimetres is that on a 1:20,000 map?
FoundationHow do six-figure and four-figure grid references differ in precision?
IntermediateThe same district appears on a 1:25,000 map and a 1:50,000 map. What is the ratio of lengths, and how many times bigger is the same square on the larger-scale map?
IntermediateA 5 km road is drawn on a 1:50,000 map. How long is it on paper?
IntermediateWhat are topographic, street and thematic maps mainly used for?
ChallengeHow should the length of a winding trail be measured on a map?
ChallengeHong Kong lies near 22 degrees north and 114 degrees east. Which two hemispheres is that?
Error redoA classmate says 1 cm² on a map equals 1 km² after multiplying by the scale once. What is wrong?

03　Answers and one-line notes

#	Answer	One-line note
1	The sides are 1,000 m and 750 m, giving 750,000 m² or 0.75 km².	Convert each side first, then multiply for the area.
2	060 + 180 = 240 degrees.	Opposite directions differ by 180 degrees, subtracting 360 if the result passes it.
3	600 × 100 ÷ 20,000 = 3 cm.	Turn metres into centimetres first, then divide by the scale denominator.
4	A six-figure reference is accurate to 100 m, while a four-figure one is only accurate to 1 km.	Two more digits sharpen the precision from a kilometre to a hundred metres.
5	Lengths are in the ratio 1:2, and areas differ by 4 times, the square of the scale.	A scale compares lengths, so areas scale with its square.
6	5,000 × 100 ÷ 50,000 = 10 cm.	Kilometres become centimetres after multiplying by 100,000, then divide by the scale.
7	Topographic maps show relief with contours, street maps show roads and transport, and thematic maps show one topic such as population or land use.	Pick the map for the task; a street map cannot show relief.
8	Lay a soft rule or thin string along the route, or split it into short straight sections and add them.	A single straight measurement underestimates a winding route.
9	The northern hemisphere and the eastern hemisphere.	North latitude places it north, east longitude places it east, so read both.
10	Wrong. Areas scale with the square of the scale, so 1 cm² on a 1:25,000 map is only 0.0625 km².	A length scales once but an area scales twice.

04　What to do after marking

After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
Repeat the same item two days later; move to the next paper only when both attempts are correct.
Parents only need the answer and note columns; there is no need to explain every item.

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