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Consider any large rectangle from which a smaller rectangular portion has been removed. The removed rectangular portion may have any orientation i.e. the remaining figure is not necessarily symmetric anymore.

Using a single cut how would you divide the given figure into two figures of equal area ?

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  • $\begingroup$ You should accept one of the proposed answers as the right solution, or comment on them and tell how they don't solve your puzzle. $\endgroup$
    – Falco
    Commented Sep 29, 2014 at 9:45
  • $\begingroup$ If you would have stated one straight cut, than only one solution is possible. $\endgroup$
    – Moti
    Commented Mar 1, 2015 at 7:17

2 Answers 2

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Simply cut through center of both rectangles. enter image description here

for the case that both centers overlaps, cut through the doubled center and with any angle.

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The solution space has 1 degree of freedom, meaning that I can make the cut with any angle I want, I just have to solve a reasonably simple differential equation to know where to place the cut.

But an easier solution is to simply cut along the line that goes through both rectangle centres, thus dividing both rectangles exactly in half, and therefore making the areas of the two halves equal.

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    $\begingroup$ And to add the obvious: those center points can easily be found as the section point of the diagonal lines. Meaning you can draw it using just a ruler. $\endgroup$
    – Tim Couwelier
    Commented Sep 10, 2014 at 9:25

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