2. The linear functions are given as

$$
y=-1, y=\frac{3}{2} x-4, y=\frac{1}{4} x-\frac{7}{2} \text { and } y=2 x+7
$$

Determine the coordinates of the vertices and the area of the regular quadrilateral that is bounded by the graphs of the given functions.
Solution. Let's denote the mentioned vertices as $A, B, C, D$ as shown in the diagram on the right. We have:

$A(-4,-1), B(2,-1), C(6,5), D(-2,3)$

The area of the figure is

$$
\begin{aligned}
P & =\frac{A E \cdot E D}{2}+\frac{(E D+B F) \cdot E B}{2}+\frac{B F \cdot h_{B F}}{2} \\
& =\frac{2 \cdot 4}{2}+\frac{(4+5) \cdot 4}{2}+\frac{5 \cdot 4}{2}=32
\end{aligned}
$$

![](https://cdn.mathpix.com/cropped/2024_06_05_ac2bd3b4ef21cfd30547g-3.jpg?height=480&width=529&top_left_y=481&top_left_x=918)