The area of a parallelogram formed by the lines ax±by±c=0 is

The given lines are ax±by±c=0 or x± c/a+y± c/b=1The vertices of rhombus are are Ac/a,0,   C−c/a, 0, B0, c/b, D0, −c/b. Therefore the diagonal AC and BD of quadrilateral ABCD are perpendicular. Hence, it is a rhombus whose area is given by 12×AC×BD=12×2ca×2cb=2c2ab