I have a 2D polygon that I want to shrink by a specific offset (A) to match a certain area ratio (R) of the original polygon. Is there a formula or algorithm for such a problem? I am interested in a simple solution for a triangle/quad but also a solution for complex polygons.

I attached an image for explanation. The original polygon is offset by A (equal-distant for each edge). A has to be chosen so that the new polygon has a specific area. In this example it should have half the area of the initial polygon.