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'Pentagonal' printed from https://nrich.maths.org/

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Square with a random point selected inside


Can you prove that the sum of the distances of any point inside a square from its sides is always equal?

Can you prove it to be true for a rectangle or a regular hexagon?
Does the hexagon need to be regular?

Can you show the same is the case for a regular pentagon?
Does the pentagon need to be regular?