Offset an irregular polygon to an area ratio (0.2)

I want to offset the sides of an irregular polygon so that the resulting area of the new smaller polygon is 20% the area of the original polygon.
All sides of the irregular polygon are offset inwards by the same amount.
How do I determine the width of the offset? Is there a formula for this?

If you wish for the new polygon to be similar to the original, but have the area of the original, then the new sides should be times as long as the original sides. This is because the area of a plane figure varies as the square of any of its linear measures.