Map scales and area factors
Convert map lengths in common units and square a length factor for corresponding areas.
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Map scales compare lengths
A scale of 1:50 000 means 1 cm on the map represents 50,000 cm, or 0.5 km, on the ground. A 6 cm route represents 3 km when measured along the corresponding route.
Area uses two length factors. A 2 cm by 3 cm rectangle on this map represents 1 km by 1.5 km, area 1.5 km². Multiplying the map’s 6 cm² by the length factor only once would be wrong.
Decide before applying a rule
A square drawing is enlarged with every length multiplied by 3. How do its perimeter and area change?
Show answer
Every boundary length triples, so perimeter triples. Each of two perpendicular dimensions triples, so area becomes nine times the original. The length scale factor and area scale factor differ.
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