Hex

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

LOGO Challenge 6 - Triangles and Stars

Recreating the designs in this challenge requires you to break a problem down into manageable chunks and use the relationships between triangles and hexagons. An exercise in detail and elegance.

Hexagon Cut Out

Weekly Problem 52 - 2012
An irregular hexagon can be made by cutting the corners off an equilateral triangle. How can an identical hexagon be made by cutting the corners off a different equilateral triangle?

Hexapentagon

Stage: 3 and 4 Short Challenge Level:

Each interior angle of a regular pentagon is $108$ degrees, whilst each interior angle of a regular hexagon is $120$ degrees. The non-regular pentagon in the centre of the diagram contains two angles which are interior angles of the regular hexagon, two angles which are interior angles of the regular hpentagon and a fifth angle, the one marked $x$. So: $x+2\times120+2\times108= 5\times108=540$. Hence $x=84$.

This problem is taken from the UKMT Mathematical Challenges.
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