How do you find the scale factor when given Area 1 and Area 2

Question

Given 2 areas, what is the scale factor going from both areas?

Answer 1

Scale factor is a ratio of linear measurements.  For example, 1 in = 1 ft means that the real distance is 12 times as much as the map distance, for example.

 

Although it is pretty confusing, scale factors do not have to be the same in two directions.  So, you could have a scale factor of 1 in : 1 ft in one direction and a scale factor of 1 in: 1 yd in the other direction.  This is often the case for advanced math formulas with exponential, logarithm, or other high-level equations.  [Special note:  this is not the same as plotting only the local points in one direction as they do with stock values on stock market news.]

 

So, if the scale in one direction is a:b and the scale in the other direction is c:d, then the First Area (ac) is really bd in size.  The ratio ("scale") of increase is bd/ac.

Answer 2

Simply divide the second area by the first area (scale

factor can be an integer or a fraction).  Given lengths

of a the sides of a rectangle, if the sides are multiplied

by a factor of "k", the corresponding areas are are

multiplied by "k²".

 

For example, given rectangle of sides 3"x5".  Area is 15in².  

Let's double the side lengths (k=2) to 6"x10".  Area is

now 60in².

 

60/15=4.......the scale factor (or k²) for area is 4, or 2².

 

Try several more examples by tripling (k=3) or quadrupling

(k=4) the 3"x5" original rectangle side lengths and determining

the corresponding scale factors for area.  You should see a 

pattern.