1. ## Proportion and scaling

...in this forum but i need help so i guess that there are many mathematics who could help me to find an aswer for the following question- the size of my paper map is one square meter and the surface area of the place in the map is 338000 square kilometers. what is the right way to count the scale for that map and what is the actual scale of the map. i mean like 1:400 or something.......

2. Originally Posted by Fraulein
...in this forum but i need help so i guess that there are many mathematics who could help me to find an aswer for the following question- the size of my paper map is one square meter and the surface area of the place in the map is 338000 square kilometers. what is the right way to count the scale for that map and what is the actual scale of the map. i mean like 1:400 or something.......
first, recall that 1 km = 1000 m.

thus, $338000 ~\text{km}^2 = 338000~(1000 \text{ m})^2 = 3.38 \times 10^{11} \text{ m}^2$

so the scale is 1:338000000000

3. Originally Posted by Fraulein
...in this forum but i need help so i guess that there are many mathematics who could help me to find an aswer for the following question- the size of my paper map is one square meter and the surface area of the place in the map is 338000 square kilometers. what is the right way to count the scale for that map and what is the actual scale of the map. i mean like 1:400 or something.......
The scale of a map refers to the proportion between lengthes of the map and the corresponding lengthes in the landscape.

Let us assume that your map is a square with the side of 1 m. Then the corresponding square in the landscape has a side of $s = \sqrt{338,000,000\ m^2}\approx 18385 \ m$

Therefore the scale of your map is 1 : 18385 which is a rather unusual format.

4. which one is the correct answer? my map is exactly one square meter which is 100x100cm.

5. Originally Posted by Fraulein
which one is the correct answer? my map is exactly one square meter which is 100x100cm.
None of them because I've made a mistake.

$1\ km^2 = (1000\ m)^2 = 1,000,000\ m^2$

Therefore the scale is

$1 : \sqrt{338,000,000,000} = 1:581,378$