Problem 6 · 2011 Math Kangaroo
Medium
Geometry & Measurement
perimeter
A regular hexagon of side-length 1, six squares and six equilateral triangles fit together as shown on the right. What is the perimeter of this tessellation?
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Answer: E — 12
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Hint 1 of 2
The whole tessellation has a 12-sided outline; every outer edge has length 1.
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Hint 2 of 2
Just count the outer edges — one per square and triangle around the rim.
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Approach: count unit edges on the outer boundary
- Around the rim the squares and triangles each contribute outer edges of length 1.
- The boundary is a regular 12-gon of unit edges, so the perimeter is 12.
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