Answered

Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Select the correct answer.
Pentagon ABCDE is similar to pentagon PQRST. If the side length of pentagon ABCDE is 6 times the side length of pentagon PQRST, which statement is true?
O A.
The area of pentagon ABCDE is 216 times the area of pentagon PQRST
B.
C.
O D.
The area of pentagon ABCDE is 12 times the area of pentagon PQRST.
The area of pentagon ABCDE is 36 times the area of pentagon PQRST
The area of pentagon ABCDE is 6 times the area of pentagon PQRST.

Sagot :

GinnyAnswer
To solve this problem, we need to understand how the areas of similar figures are related given a scale factor.

Let the side length of pentagon PQRST be [tex]\( s \)[/tex]. Therefore, the side length of pentagon ABCDE is [tex]\( 6s \)[/tex] (since it's given that ABCDE is 6 times the side length of PQRST).

Given that the shapes are similar, the ratio of their areas is proportional to the square of the scale factor of their corresponding side lengths.

Here, the scale factor is 6. So to find the area ratio, we square the scale factor:
[tex]\[ \text{Area ratio} = 6^2 = 36 \][/tex]

Thus, the area of pentagon ABCDE is 36 times the area of pentagon PQRST.

From the given statements, the correct answer is:
C. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.