In the diagram, $A B C D$ is a square with a side length of 10 . If $A Y=C X=8$, the area of the shaded region is
(A) 16
(D) 48
(B) 20
(E) 24
(C) 40

![](https://cdn.mathpix.com/cropped/2024_04_20_e85ef69091c57cb633f3g-123.jpg?height=273&width=266&top_left_y=1197&top_left_x=1366)
Solution 1

Since $A Y=C X=8$, then we must have $D Y=B X=2$, and so $D Y B X$ is a parallelogram.

If we rotate the picture by $90^{\circ}$ clockwise, then we can see that $D Y B X$ is a parallelogram with a base of length 2 and a height of 10, ie. it has an area of $b h=2(10)=20$.

![](https://cdn.mathpix.com/cropped/2024_04_20_688a3b42f69739f2e244g-223.jpg?height=374&width=361&top_left_y=1415&top_left_x=1359)

## Solution 2

The area of the shaded region is equal to the area of the entire square minus the areas of the two triangles. Each of the two triangles $B A Y$ and $D C X$ is right-angled with one leg of length 10 and the other of length 8 .

Therefore,

$$
\begin{aligned}
& =(10)^{2}-2\left[\frac{1}{2}(8)(10)\right] \\
& =100-2[40] \\
& =20
\end{aligned}
$$

$$
\text { Area of shaded region }=\text { Area of square }- \text { Area of triangles }
$$

ANSWER: (B)