Finding the area under a quadrilateral whose sides are given by four linear equations. Let there be $4$ equations, namely:


*

*$y=m_1x+c_1$

*$y=m_2x+c_2$

*$y=m_3x+c_3$

*$y=m_4x+c_4$


Assuming that these $4$ lines form a quadrilateral, how do I calculate the area of the quadrilateral?
One way I thought was that any quadrilateral can be made into two triangles by joining its opposite vertices.
Then I can calculate the areas of the individual triangles.
However that would be a long and tedious way. 
Can there be a simple way?

If two pairs of lines are parallel then they will have an equal slope . Find intersection of points which intersect the lines at two points here let us assume $m_1||m_3$ and same for other two then find their points of intersections and then find distance between the three adjacent points by using distance formula.note its for quadrilatetals formed by two pairs of parallel lines. We also have formula for distance between parallel lines $\frac{|c_2-c_1|}{\sqrt{a^2+b^2}}$ where $c_1,c_2$ are constants and $a,b$ are any arbitrary constants.
