The scale of a map is 1:300 000
Find the actual area of the village, in km^2, if the area on the map is 3cm^2
It tells us that 1cm on the map gives 300,000 cm in real life.
If we had a square of side length 1cm, it would correspond to a square of side lengths 300,000cm. So a square with area $\displaystyle 1cm \times 1cm = 1cm^2$ would correspond to a square of area $\displaystyle 300,000cm \times 300,000cm = 90,000,000,000cm^2$.
So if the area on the map is $\displaystyle 3cm^2$ then it would correspond to an area of $\displaystyle 3 \times 90,000,000,000cm^2 = 270,000,000,000cm^2$.
Since there are 100cm in 1 metre, there are $\displaystyle 100^2cm^2=10,000cm^2$ in $\displaystyle 1m^2$.
So that means that $\displaystyle 270,000,000,000cm^2 = 27,000,000m^2$.
Since there are 1000m in 1km, there are $\displaystyle 1000^2m^2 = 1,000,000m^2$ in $\displaystyle 1km^2$.
So $\displaystyle 27,000,000m^2 = 27km^2$.
Therefore the actual area that is represented by this map is $\displaystyle 27km^2$.