The coordinates of the vertices of a pentagon are $A(0 ; 0), B(11 ; 0), C(11 ; 2), D(6 ; 2), E(0 ; 8)$. Write the equation of the line that is parallel to the $y$-axis and divides the area of the pentagon in half.
Let's use the notations from the figure.

![](https://cdn.mathpix.com/cropped/2024_05_02_cb8b6fb459fb998a2f9ag-1.jpg?height=762&width=746&top_left_y=221&top_left_x=684)

Therefore,

$$
T_{A B C D E}=30+10=40
$$

Let $e$ be the line that satisfies the conditions. (This line intersects the $x$-axis at point $K$.) Let the distance $A K$ be denoted by $d$. Since $T_{G B D C}=10$ and $\frac{1}{2} T_{A B C D E}=20$, it follows that $06 > d_{2}$, so $d_{2}$ satisfies our conditions. The line $e$ thus passes through the point $K(8-2 \sqrt{6} ; 0)$; its equation is:

$$
x=8-2 \sqrt{6} \quad(\approx 3.1)
$$