Sure, let's break this down step-by-step.
When dealing with similar polygons, the areas of these polygons are related to the square of the ratios of their corresponding side lengths. This is important and can be derived from the properties of similar polygons.
1. Determine the side length ratio: The given ratio of the corresponding side lengths is 5:9.
2. Square the side length ratio: To find the ratio of their areas, we need to square the lengths of the sides. This is because the areas of similar polygons are proportional to the squares of their corresponding side lengths.
- The square of the ratio 5:9 is calculated as follows:
- [tex]\(5^2\)[/tex]:[tex]\(9^2\)[/tex]
- [tex]\(25\)[/tex]:[tex]\(81\)[/tex]
3. Conclusion: Based on the squared ratio of the side lengths, the ratio of the areas of the two similar polygons is 25:81.
So, the best answer from the choices provided is:
C. 25:81
