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

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- Oct 31st 2008, 08:11 PMhelloyingMaps
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 - Nov 1st 2008, 07:25 PMProve It
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 $\displaystyle 27km^2$. - Nov 1st 2008, 07:29 PMhelloying
OH I SEE! thank you very much. I have been very stupid. i understand now