Final answer:
To find the scale factor between similar figures, compare their corresponding linear dimensions; the ratio is the scale factor. For areas, the ratio is the square of the linear scale factor. Use proportions to solve for unknowns using the scale factor.
Step-by-step explanation:
When we're looking to find the scale factor from a larger figure to a smaller figure, we simply compare the dimensions of two similar polygons. Assuming we have the lengths of corresponding sides of the polygons (or any linear measures), the scale factor is the ratio of any side length of the larger polygon to the corresponding side length of the smaller one. The sides should be corresponding and measured in the same units. Moreover, when comparing the areas of the two similar polygons, the ratio of the areas is the square of the linear scale factor.
For example, to find the missing actual dimension given a scale factor of 2":3' and a scale measurement of 6", we start by writing the proportion such as scale/actual. If the scale factor between a model and the actual object is 2:1, and 3 inches on the model represents 12 feet in reality, first writing out the ratio helps in determining the scale factor, which in this case would be 3 inches/12 feet. This simplifies to a scale factor of 1:48 when we convert feet to inches (since 12 feet = 144 inches, and 3 inches/144 inches = 1/48).
To summarize a process: if given dimensions for similar figures, we can establish the scale factor directly from the dimensions. If we need to determine an unknown dimension, we can set up a proportion that utilizes the known scale factor. And, when it comes to areas, the relationship of their ratio is the linear scale factor squared.