Given equation of straight lines are
$y=2 x, y=2 x+1, y=-7 x$
and $y=-7 x+1$
Now, draw these lines on paper, we get
Coordinates of $O \to (0,0), B \to (0,1), C\to \left(\frac{1}{9}, \frac{2}{9}\right)$
and $A \rightarrow\left(-\frac{1}{9}, \frac{7}{9}\right)$
$\therefore $ Area of parallelogram
$=2 \times$ Area of $\Delta \,OBC$
$=2 \times \frac{1}{2}\left|x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)\right|$
$=\left|0+0+\frac{1}{9}(0-1)\right|=\frac{1}{9}$
