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Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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LOGO Challenge - Following On

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?


Stage: 4 Challenge Level: Challenge Level:1

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 (half the perimeter)?

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?