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Of All the Areas

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

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LOGO Challenge 5 - Patch

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

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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.

Angle of Overlap

Stage: 3 and 4 Short Challenge Level: Challenge Level:1
Angle CBE = (180-75-60)degrees = 45 degrees
Angle DEB= (180-65-60)degrees = 55 degrees
Angle GHB= (45+55)degrees = 100degrees (exterior angle of a triangle)
AngleHGC = (100-60)degrees = 40 degrees (exterior angle of a triangle)

This problem is taken from the UKMT Mathematical Challenges.
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