Maps

**helloying** · October 31st 2008, 08:11 PM

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

**Prove It** · November 1st 2008, 07:25 PM

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 $27km^2$ .

**helloying** · November 1st 2008, 07:29 PM

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

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