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Geometry Level 4

A cube is sliced into halves in such a way that the cut is a _ _ .

The statement above is true. Which of the following can not be written to the line?

Not regular pentagon Not regular hexagon Regular pentagon Trapezium, but not parallelogram Parallelogram, but not rectangle Regular triangle Not regular triangle Regular hexagon

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1 solution

Áron Bán-Szabó
Aug 25, 2017

I didn't make an example for a not regular hexagon, but it easy find one from the regular hexagon.

If the cut is a pentagon, then the pentagon touches exactly five faces, so it touches to parallel faces (for sure). So the pentagon will have two parallel sides, therefore it can't be regular.

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