4. Two regular hexagons are placed next to each other within a parallelogram as indicated in the figure. The area of the parallelogram is 1.

What is the combined area of the two gray shaded regions?

![](https://cdn.mathpix.com/cropped/2024_04_17_01cb006263f00c7722c1g-1.jpg?height=197&width=396&top_left_y=2529&top_left_x=1521)
A) $\frac{1}{3}$
B) $\frac{2}{5}$
C) $\frac{5}{12}$
D) $\frac{3}{7}$
E) $\frac{1}{2}$
A4. E) $\frac{1}{2}$ We can divide each hexagon into six equal-sized equilateral triangles. With another twelve of these equilateral triangles, we can complete the parallelogram, see the figure. We now see that the two gray areas together cover exactly $\frac{12}{24}$ of the parallelogram. The combined area of the gray regions is thus $1 \cdot \frac{12}{24}=\frac{1}{2}$.

![](https://cdn.mathpix.com/cropped/2024_04_17_fc21619166b069277c26g-1.jpg?height=203&width=397&top_left_y=2263&top_left_x=838)