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 6 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 12 times the area of pentagon pqrst. d. the area of pentagon abcde is 216 times the area of pentagon pqrst.

Explanation:

Step1: Recall area - ratio formula for similar figures

For similar figures, if the ratio of side - lengths is $k$, the ratio of areas is $k^{2}$. Here $k = 6$.

Step2: Calculate the ratio of areas

The ratio of the area of pentagon $ABCDE$ to the area of pentagon $PQRS$ is $k^{2}=6^{2}=36$.

Answer:

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