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?

Re: Offset an irregular polygon to an area ratio (0.2)

If you wish for the new polygon to be similar to the original, but have $\displaystyle \frac{1}{5}$ the area of the original, then the new sides should be $\displaystyle \frac{1}{\sqrt{5}}$ 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.