Unit Posttest Select the correct answer. Pentagon \( A B C D E \) is similar to pentagon \( P Q R S T \). If the side length of pentagon \( A B C D E \) is 6 times the side length of pentagon \( P Q R S T \), which statement is true? A. The area of pentagon \( A B C D E \) is 6 times the area of pentagon \( P Q R S T \). The area of pentagon \( A B C D E \) is 12 times the area of pentagon \( P Q R S T \). C. The area of pentagon \( A B C D E \) is 36 times the area of pentagon \( P Q R S T \). D. The area of pentagon \( A B C D E \) is 216 times the area of pentagon \( P Q R S T \).

To determine the correct statement about the areas of the similar pentagons, let's analyze the given information: - **Pentagons \( A B C D E \) and \( P Q R S T \) are similar.** - **The side length of pentagon \( A B C D E \) is 6 times the side length of pentagon \( P Q R S T \).** ### Understanding Similarity and Area Scaling When two polygons are similar, the ratio of their areas is the square of the ratio of their corresponding side lengths. This relationship can be expressed as: \[ \text{Area Ratio} = \left(\frac{\text{Side Length of } A}{\text{Side Length of } P}\right)^2 \] Given that the side length of \( A B C D E \) is 6 times that of \( P Q R S T \): \[ \text{Area Ratio} = 6^2 = 36 \] ### Conclusion The area of pentagon \( A B C D E \) is **36 times** the area of pentagon \( P Q R S T \). **Correct Answer:** C. The area of pentagon \( A B C D E \) is 36 times the area of pentagon \( P Q R S T \).