Question

What is the scale factor of the similar polygons below?
What is the scale factor of their perimeters?
What is the scale factor of their areas?

ABC ~ DEF

ABC = 18, 21, 24
DEF = 6, 7, 8

Answer 1

To find the scale factor of similar polygons ABC and DEF, we need to compare their corresponding side lengths.

1. **Finding the Scale Factor**:
The scale factor is calculated by taking the ratio of the lengths of corresponding sides.

For the given polygons:
- For side lengths of ABC and DEF:
- \( \frac{18}{6} = 3 \)
- \( \frac{21}{7} = 3 \)
- \( \frac{24}{8} = 3 \)

Since all corresponding sides have the same ratio, the scale factor of the polygons ABC and DEF is **3**.

2. **Scale Factor of their Perimeters**:
The scale factor of the perimeters of similar figures is the same as the scale factor of their corresponding side lengths.
Therefore, the scale factor of the perimeters is also **3**.

3. **Scale Factor of their Areas**:
The scale factor of the areas of similar figures is equal to the square of the scale factor of their corresponding side lengths.
Thus, if the scale factor of the side lengths is **3**, then the scale factor of the areas is:
\[
3^2 = 9
\]

In summary:
- Scale factor of the polygons (side lengths): **3**
- Scale factor of their perimeters: **3**
- Scale factor of their areas: **9**