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Question:

# A map has a scale of 4 cm to 1 km. What is the actual area of a lake on ground which is represented as an area of $60cm^2$ on the map?

A $3.75km^2$
explanation

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:
$4^2cm$ square: $1^2km$ square, which gives $16cm^2 \div 1km^2$
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: $\frac{\mathrm{16cm^2} }{\mathrm{1km^2}}=\frac{\mathrm{60cm^2} }{\mathrm{xkm^2}}$ , where x is the unknown actual area. Note that every proportion you write should maintain consistency in the ratios described. In this case, $cm^2$ both occupy the numerator, and $km^2$ both occupy the denominator. The proportion will not work if one $cm^2$ was written in the numerator and the other written in the denominator. Cross-multiply and isolate to solve for the unknown area x: $x \times \frac{\mathrm{16cm^2} }{\mathrm{1km^2}}= 60cm^2$, which simplifies to $x=60cm^2 \times \frac{\mathrm{1km^2} }{\mathrm{16cm^2}}$, which simplifies to $x=3.75km^2$.

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