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Math Help - Offset an irregular polygon to an area ratio (0.2)

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    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?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    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 \frac{1}{5} the area of the original, then the new sides should be \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.
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