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Question:

A map has the scale of 4 cm to 1 km. What is the actual area of a lake on ground which is represented as an area of $1327_w48_h16.png$ on the map?

A $7943_w64_h16.png$
Explaination

The problem gives the scale of 4cm:1km, 4 cm on the map represents an actual distance of 1 km.
As the question asks for the relationship between the areas, it is first necessary to rewrite the scale ratio in terms of units squared:
$9933_w40_h17.png$ square: $2505_w41_h17.png$ square, which gives $7654_w111_h17.png$
Using the ratio of the areas and the map area given in the problem, a proportion can be written that enables calculation of the actual area: $6004_w125_h42.png$ , where x is the unknown actual area. Note that every proportion you write should maintain consistency in the ratios described. In this case, $5530_w30_h16.png$ both occupy the numerator, and km2 both occupy the denominator. The proportion will not work if one cm2 was written in the numerator and the other written in the denominator. Cross-multiply and isolate to solve for the unknown area x: $9564_w157_h42.png$, which simplifies to $5141_w156_h42.png$, which simplifies to $7330_w98_h16.png$