2025 AMC 8 Problem 10

In the figure below, ABCD is a rectangle with sides of length AB = 5 inches and AD = 3 inches. Rectangle ABCD is rotated 90^\circ clockwise around the midpoint of side DC to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles?

\textbf{(A)} 21 \qquad \textbf{(B)} 22.25 \qquad \textbf{(C)} 23 \qquad \textbf{(D)} 23.75 \qquad \textbf{(E)} 25

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