2016 Fermat Problem 10

In the diagram, square PQRS has side length 2. Points W, X, Y, and Z are the midpoints of the sides of PQRS. What is the ratio of the area of square WXYZ to the area of square PQRS?

\textbf{(A)}\ 1:2\quad \textbf{(B)}\ 2:1\quad \textbf{(C)}\ 1:3\quad \textbf{(D)}\ 1:4\quad \textbf{(E)}\ \sqrt{2}:2

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