Finding the actual area represented on a map 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
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).
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)