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This question appears in a kid's math book. Am I missing some obvious answer?

I can't find a way to draw a line that divides the area evenly.

enter image description here

nuggethead
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2 Answers2

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Any line between the red ones cuts the total area in half. The simplest case would be a vertical line.

Christian
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  • So yes, I was missing something obvious! Thank you! – nuggethead Sep 29 '21 at 23:56
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    In fact both red lines can be rotated further about their intersection: the one with positive slope until it reaches a slope of $\frac{2}{3}$, and the one with negative slope until it reaches a slope of $\frac{-4}{3}$. – A.J. Sep 30 '21 at 04:05
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Here's another way it could be done.

Notice in the picture, if we were to ignore the blue squares, the rest of the image has 2-fold rotational symmetry and so any line which passes through the centre of rotation will bisect it.
enter image description here

In particular if we choose the diagonal line from top left to bottom right, we see that this will put two of the blue squares above the line and two of them below.

enter image description here

hexomino
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  • Yes, but the instructions don't permit moving the squares around – nuggethead Sep 30 '21 at 16:25
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    @nuggethead You don't have to move any squares around, the red line above bisects the area of the shape. The rest is just a proof of that fact. – hexomino Sep 30 '21 at 16:50