Scale Factor

Here, I will be using similar polygons (circles) and showing their scale factors for units and units squared. Here are two ordinary circles, one with radius of 6, and one with radius of 10. Their scale factor is 6 divided by 10, and that simplified is 3:5.

Now when we find the circumferences of the two circles, their ratio should be the same as the ratio of the radii.

The circumferences of the two circles are 37.68 and 62.86. When we divide 37.68 by 62.86, we get .60, which is equal to 3 divided by 5. 

The areas of the circles should be in the scale factor of k squared, in other words, 3 squared / 5 squared.  The scale factor for the areas of the circles should be 9:25.

The area for the first circle is 112.99 square cm, and the area for the second circle is 314.45 square cm. If we divide 112.99 by 314.45, we get .36, which is the same as 9/25. This demonstrates that if we have any two similar polygons, any length measured in units is in the scale factor k, and anything measured in units squared is in the scale factor k squared. (~DM5)