Example 2

Determine the scale factor that was used to transform the large octagon into the small octagon. Express your scale factor as a fraction and as a percent.

  • Start by choosing corresponding side lengths.

Note: Choosing the smallest units like 3 units (in the large octagon) and 1 unit (in the small octagon) makes it easier to state the scale factor in lowest terms because there is no need to reduce the resulting fraction.

  • The scale factor as a fraction is , which is 33.3% as a percent.

Example 3

The actual length of an extra-long sewing needle is 8 cm. The length of the needle in a scale diagram is 12 cm.

  • What is the scale factor of the diagram?
  • Does the scale factor suggest the diagram of the needle is larger or smaller than the actual needle?

The scale factor is 1.5.
The scale factor tells us that the diagram is an enlargement of the actual needle.