Problem 10 (2025 AMC 8)

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 about the midpoint of side $DC$ to give a second rectangle. What is the total area, in square inches, covered by the two overlapping rectangles? [See figure in original PDF]