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.

Question

03-06-2024
Mathematics

Answered

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.

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-03T11:11:04-04:00

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.