College

We appreciate your visit to Regular pentagons A and B are similar The apothem of pentagon A is equal to the radius of pentagon B Compare their areas. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Regular pentagons A and B are similar. The apothem of pentagon A is equal to the radius of pentagon B. Compare their areas.

Answer :

Final answer:

When two polygons are similar, their corresponding sides are proportional, and their corresponding angles are congruent. The areas of pentagons A and B will be in the same ratio as the squares of their side lengths.

Explanation:

When two polygons are similar, their corresponding sides are proportional, and their corresponding angles are congruent.

In this case, regular pentagons A and B are similar. The apothem of pentagon A is equal to the radius of pentagon B.

Since the apothem of pentagon A is equal to the radius of pentagon B, their corresponding sides are proportional. This means that the ratio of their areas will be equal to the ratio of the squares of their corresponding side lengths.

Given that the apothem and radius are equal, the ratio of their areas will be equal to the square of the ratio of their side lengths:

Area of pentagon A / Area of pentagon B = (Side length of pentagon A / Side length of pentagon B)2

So, the areas of pentagons A and B will be in the same ratio as the squares of their side lengths.

Thanks for taking the time to read Regular pentagons A and B are similar The apothem of pentagon A is equal to the radius of pentagon B Compare their areas. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada