Problem 9 · 2011 Math Kangaroo
Medium
Geometry & Measurement
perimeter
Given are a regular hexagon with side-length 1, six squares and six equilateral triangles arranged as shown. What is the perimeter of this tessellation?
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Answer: C — 12
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Hint 1 of 2
The squares and triangles all have side length 1, so every outer edge has length 1.
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Hint 2 of 2
Just count how many unit edges form the outer boundary of the whole tiling.
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Approach: count unit edges on the outer boundary
- All pieces share the hexagon's side length 1, so each exposed edge is 1 unit long.
- The outer boundary of the star-shaped tiling is a twelve-sided outline.
- Each of those 12 outer edges has length 1.
- Perimeter = 12, choice (C).
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