Question

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? a. the area of pentagon abcde is 12 times the area of pentagon pqrst. b. the area of pentagon abcde is 36 times the area of pentagon pqrst. c. the area of pentagon abcde is 216 times the area of pentagon pqrst. d. the area of pentagon abcde is 6 times the area of pentagon pqrst.

Explanation:

Step1: Recall area - ratio formula for similar figures

If two similar figures have a side - length ratio of \(a:b\), the ratio of their areas is \(a^{2}:b^{2}\). Let the side - length of pentagon \(PQRST\) be \(x\) and the side - length of pentagon \(ABCDE\) be \(6x\).

Step2: Calculate the area ratio

The ratio of the side - lengths of pentagon \(ABCDE\) to pentagon \(PQRST\) is \(6:1\). Then the ratio of the area of pentagon \(ABCDE\) to the area of pentagon \(PQRST\) is \(6^{2}:1^{2}=36:1\). That is, the area of pentagon \(ABCDE\) is 36 times the area of pentagon \(PQRST\).

Answer:

B. The area of pentagon \(ABCDE\) is 36 times the area of pentagon \(PQRST\)