Find the area of the closed region D formed by the lines $x + y = c$ ,
$x + y = d$, $y = ax$, and $y = bx$ where $(0 < c < d, 0 < a < b)$ by first transforming it into a rectangle with area D' with sides d - c and b - a in the u-v plane and then via double integration.

Attempt at a solution: I found the variable relationship to be $x=\frac{u}{1+v}$ and $y=\frac{\left(u\cdot v\right)}{1+v}$ but am unable to form the double integral as the closed region D seems to be neither horizontally nor vertically simple.  

[![Graphical representation of the regions](https://i.stack.imgur.com/GINw0.jpg)](https://i.stack.imgur.com/GINw0.jpg)