My problem is that I need to find the average length $L$ of $i$ infinite parallel lines within a triangle, which can be at any angle $\theta$, between $0$ and $\pi$. Known are the co-ordinates of the corners of the triangle (labelled $x_1y_1$, $x_2y_2$, $x_3y_3$).
I have a method, which finds the area of the shape, and dividing by the perpendicular length between the extremes of these parallel lines, but this method isn't ideal as it gives three different equations, depending on theta (at least the way I have solved it).