Question

The scale of a map is 1:1000. What is the area, in cm2, on the map of a lake of area 5000 cm2?

Answer 1

area grows as the square of the scale, so the area are in the ratio
1:1000^2
so the map has area
5000/1000^2 = 5/1000 = 1/200 = 0.005 cm^2