Finding the actual area represented on a map

Question

This question is similar to finding the actual distance represented on a map. The question is:

Find the actual area, in m², represented by 1cm² on the map. The scale of map is 1: 180,000

Answer 1

A 1 cm by 1 cm square on the map represents a 180,000 cm by 180,000 cm region of land. That is, a 1,800 m by 1,800 m region of land. Its area is 3,240,000 square meters (1,800 times 1,800 is 3,240,000).

Answer 2

If you enlarge the map into the land by a similarity transformation, then the scaling factor will be $180 000$ -- i.e., all lengths are scaled by $180 000.$ Hence the area factor will be $180 000^2.$ That is, all areas $A$ on the map will map into $180 000×180 000A$ on land.

Answer 3

Calculate an actual area in Km2 represented by 40 cm2 on a map, the scale of the map given as 1:50,000. Solution: As 1 cm in the map represents 50,000 cm on ground therefore 1 cm x 1 cm = 50,000cm x 50,000 cm 1 cm2 (on map) =2,500,000,000 cm2 (on ground) = 2,500,000,000/(100,000x100,000) 1 cm2 (on map) = 0.25 km2 (on ground) 40 cm2 (on map) =40 x 0.25 km2 = 10 km2 (on ground)