find the area of a parallelogram with the sides are given using the fourth standard equation of straight line

Question

the sides of a parallelogram are on the lines $$x-3y+20=0,\\ x+y+6=0,\\ x-3y-10=0 \text{ and} \\ x+y+2=0.$$ Find its area. solve using the fourth standard equation of the straight line.

Answer 1

A less mysterious answer than rlgordonma's would be to solve for the four intersections (four sets of 2x2 linear systems of equations; 3 will do in fact), and use Heron's formula for the area of one of the resulting triangles, twice that is your answer.