AMC 10 2022a Problem 10

Daniel finds a rectangular index card and measures its diagonal to be $8$ centimeters. Daniel then cuts out equal squares of side $1$ cm at two opposite corners of the index card and measures the distance between the two closest vertices of these squares to be $4\sqrt{2}$ centimeters, as shown below. What is the area of the original index card?

$\textbf{(A) } 14 \textbf{(B) } 10\sqrt{2} \textbf{(C) } 16 \textbf{(D) } 12\sqrt{2} \textbf{(E) } 18$