1. ## Maps

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

2. Originally Posted by helloying
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 $1cm \times 1cm = 1cm^2$ would correspond to a square of area $300,000cm \times 300,000cm = 90,000,000,000cm^2$.

So if the area on the map is $3cm^2$ then it would correspond to an area of $3 \times 90,000,000,000cm^2 = 270,000,000,000cm^2$.

Since there are 100cm in 1 metre, there are $100^2cm^2=10,000cm^2$ in $1m^2$.

So that means that $270,000,000,000cm^2 = 27,000,000m^2$.

Since there are 1000m in 1km, there are $1000^2m^2 = 1,000,000m^2$ in $1km^2$.

So $27,000,000m^2 = 27km^2$.

Therefore the actual area that is represented by this map is $27km^2$.

3. OH I SEE! thank you very much. I have been very stupid. i understand now