2017 Cayley Problem 22

In the diagram, square PQRS has side length 42 and is divided into four non-overlapping rectangles. If each of these four rectangles has the same perimeter, what is the area of the shaded rectangle?

\textbf{(A)}\ 252\quad \textbf{(B)}\ 432\quad \textbf{(C)}\ 441\quad \textbf{(D)}\ 490\quad \textbf{(E)}\ 540

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.