In the diagram, $A B C D$ is a square with side length 6 , and $W X Y Z$ is a rectangle with $Z Y=10$ and $X Y=6$. Also, $A D$ and $W X$ are perpendicular. If the shaded area is equal to half of the area of $W X Y Z$, the length of $A P$ is
(A) 1
(B) 1.5
(C) 4
(D) 2
(E) 2.5

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-069.jpg?height=295&width=422&top_left_y=763&top_left_x=1296)
The area of rectangle $W X Y Z$ is $10 \times 6=60$.

Since the shaded area is half of the total area of $W X Y Z$, its area is $\frac{1}{2} \times 60=30$.

Since $A D$ and $W X$ are perpendicular, then the shaded area has four right angles, so is a rectangle.

Since square $A B C D$ has a side length of 6 , then $D C=6$.

Since the shaded area is 30 , then $P D \times D C=30$ or $P D \times 6=30$ or $P D=5$.

Since $A D=6$ and $P D=5$, then $A P=1$.

ANSWER: (A)