Create polygon with certain area percentage of larger existing polygon

I need to create polygons with a certain area percentage of an existing, larger polygon by offsetting one edge.

In the below picture, I have the green polygon and I need to create the red polygon. The red polygon’s area needs to be a certain percentage that I am able to define (let’s say 70%) of the green polygon’s area. I’d like to do that by only offsetting one edge (the blue distance).

I’ve tried to start a couple of different ways but haven’t gotten far. Thanks in advance.

Will the shapes always be quadrilaterals, or are you looking for something that will work for more general shapes?

It would be great if it could work for more complex shapes. For example how far would I have to offset the green lines in the directions shown below

For simple cases the rate of change in area relative to the offset could be found using the tangent of the angle between the 2 lines the moving edge is sliding along, and from this you can find how far you need to move it.
For more general cases you could solve it with Kangaroo like this, which lets you set the fixed larger polygon, the area ratio, which corners to keep fixed and which edges to make parallel:
polygonareas.gh (18.4 KB)

I am admittedly not super familiar with Kangaroo. I keep running into this issue where the lines are switching from their input lines.

It’s not clear to me from that image which is the side you are trying to offset and which parts are fixed.
Can you post the file?
The definition was assuming the initial geometry is at least very roughly near the right ratio so it doesn’t have to jump between segments.
If you want to be able to start further away from your target ratio it might be necessary to fix points to specific segments of the boundary rather than the whole curve.

Sorry I realize that example changed from the previous one!

Here is the file. Essentially, I need to move the specific side of the dotted polygon in the direction of the green arrow IF the area of the dotted polygon is more than 70% of the area of the red polygon that it is inside. And I need to move the line so the new area of the dotted polygon would be 70% of the area of the red polygon.

Thanks so much for all this help, really appreciate it.

Offset Polygon_2020.07.28.3dm (82.6 KB)