Problem

2019 Pascal Problem 20

In the diagram, square $PQRS$ has side length $40$ . Points $J$ , $K$ , $L$ , and $M$ are on the sides of $PQRS$ , as shown, so that $JQ = KR = LS = MP = 10$ . Line segments $JZ$ , $KW$ , $LX$ , and $MY$ are drawn parallel to the diagonals of the square so that $W$ is on $JZ$ , $X$ is on $KW$ , $Y$ is on $LX$ , and $Z$ is on $MY$ . What is the area of quadrilateral $WXYZ$ ?

$\textbf{(A)}\ 280\quad$ $\textbf{(B)}\ 200\quad$ $\textbf{(C)}\ 320\quad$ $\textbf{(D)}\ 240\quad$ $\textbf{(E)}\ 160$

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 Pascal contests here.

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Difficulty —

Category: Pascal
Points: 2
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