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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?

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Pentagonal

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 hexagon?

Star Gazing

Stage: 4 Challenge Level: Challenge Level:1

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