We have two pairs of parallel lines in R^2 defined by the linear equations below:

a1x + b1y = r1

a1x + b1y = s1

a2x + b2y = r2

a2x + b2y = s2

We assume that these lines enclose a parallelogram P. Find the very simplest formula for the area of P in terms of a1, b1, a2, b2, r1, r2, s1, s2.

If it is R^2, why are there four formulas? Any help with this