How to find the scale factor of a polygon?

Understand the Problem

The question is asking how to determine the scale factor of a polygon, which involves understanding the relationship between the sizes of similar polygons or their corresponding sides.

Answer

The scale factor is $2$.

Steps to Solve

Identify Corresponding Sides Start by identifying the lengths of corresponding sides of the two similar polygons. For example, if polygon A has a side of length 4 units and polygon B has a corresponding side of length 8 units, you'll use these lengths in the next step.
Calculate the Scale Factor The scale factor is found by dividing the length of a side of the larger polygon by the length of the corresponding side of the smaller polygon. For our example, the calculation would be:

$$ \text{Scale Factor} = \frac{\text{Length of Side in Polygon B}}{\text{Length of Side in Polygon A}} = \frac{8}{4} $$

Simplify the Scale Factor After calculating the scale factor, simplify the fraction if possible. In our example:

$$ \frac{8}{4} = 2 $$

So the scale factor is 2.

Verify with Other Corresponding Sides To ensure accuracy, check other pairs of corresponding sides to confirm the calculated scale factor is consistent across the polygon. If all pairs yield the same scale factor, then it is validated.

The scale factor is 2.

More Information

The scale factor is a crucial concept in geometry, particularly when dealing with similar shapes. It tells you how many times larger or smaller one shape is compared to another. Here, a scale factor of 2 means polygon B is 2 times larger than polygon A.

Tips

Using Non-Corresponding Sides: Always ensure you are comparing corresponding sides. Using mismatched pairs will lead to incorrect scale factors.
Not Simplifying Fractions: Ensure you simplify the scale factor fraction, as it may not be in its simplest form initially.

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