In the diagram, square $A B C D$ has a side length of 4 . What is the total area of the shaded regions?
(A) 4
(B) 8
(C) 9
(D) 12
(E) 16

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-117.jpg?height=407&width=366&top_left_y=271&top_left_x=1446)
In the diagram, the square is divided into four rectangles, each of which has been divided in half to form two identical triangles. So in each of the four rectangles, the area of the shaded triangle equals the area of the unshaded triangle. Thus, the area of the shaded region is $\frac{1}{2}$ of the overall area of the square, or $\frac{1}{2}$ of 16 square units, or 8 square units.

Answer: (B)