My textbook states that the area of a parallelogram bounded by $y=m\_1x+c\_1$, $y=m\_1x+c\_2$, $y=m\_2x+d\_1$, and $y=m\_2x+d\_2$ is:

$$area=\left|\frac{(c\_1-c\_2)(d\_1-d\_2)}{m\_1-m\_2}\right|$$

I don't understand how to derive this result. The only thing I can do with these lines is take their perpendicular distance, which is useless because the parallelogram is inclined and not rectangular. Plus, I'll be stuck with a $\sqrt{1+m^2}$ in the denominator which I can't find way to get rid of.

Any advice is appreciated. Thanks!