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Answer :
Since pentagons ABCDE and PQRST are similar, the ratio of any pair of corresponding side lengths is constant. Let the ratio of a side of ABCDE to a corresponding side of PQRST be [tex]$6:1$[/tex]. For similar figures, the ratio of their areas is the square of the ratio of their corresponding side lengths. Therefore, the area of pentagon ABCDE compared to the area of pentagon PQRST is given by:
[tex]$$
\left(6\right)^2 = 36.
$$[/tex]
This means that the area of pentagon ABCDE is [tex]$36$[/tex] times the area of pentagon PQRST.
Thus, the correct answer is:
[tex]$$\textbf{D. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.}$$[/tex]
[tex]$$
\left(6\right)^2 = 36.
$$[/tex]
This means that the area of pentagon ABCDE is [tex]$36$[/tex] times the area of pentagon PQRST.
Thus, the correct answer is:
[tex]$$\textbf{D. The area of pentagon ABCDE is 36 times the area of pentagon PQRST.}$$[/tex]
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