2025 AMC 10A Problem 15

In the figure below, ABEF is a rectangle, AD \perp DE, AF = 7, AB = 1, and AD = 5. What is the area of \triangle ABC?

\textbf{(A)} \dfrac{3}{8} \qquad \textbf{(B)} \dfrac{4}{9} \qquad \textbf{(C)} \dfrac{1}{8}\sqrt{13} \qquad \textbf{(D)} \dfrac{7}{15} \qquad \textbf{(E)} \dfrac{1}{8}\sqrt{15}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.