Two 12-sided polygons are similar. A side of the larger polygon is 3 times as long as the corresponding side of the smaller polygon. What is the ratio of the area of the larger polygon to the area of the smaller polygon?

When two polygons are similar, the ratio of their areas is the square of the ratio of their corresponding side lengths.

Given that the side of the larger polygon is 3 times as long as the corresponding side of the smaller polygon, the ratio of the side lengths is \( \frac{\text{Side of larger polygon}}{\text{Side of smaller polygon}} = 3 \).

The ratio of the areas of the polygons is the square of the ratio of the side lengths:

\[
\text{Ratio of areas} = 3^2 = 9
\]

Thus, the ratio of the area of the larger polygon to the area of the smaller polygon is \( 9:1 \).

Would you like more details or have any questions?

Here are 5 related questions:

1. What is the general formula for finding the area ratio of similar polygons?
2. How does the number of sides affect the similarity of polygons?
3. Can this method be used for non-polygonal shapes? Why or why not?
4. What would the area ratio be if the side length ratio was 4:1?
5. How do you find the side length ratio if only the area ratio is known?

**Tip:** Remember, when working with similar figures, the ratio of areas is always the square of the ratio of corresponding sides.

Understand how to calculate the ratio of areas for similar polygons with a detailed solution. Learn the concept of similarity in polygons and the formula for calculating area ratios based on side length ratios. Suitable for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation