Problem 6 · 2018 Math Kangaroo
Hard
Geometry & Measurement
area-decompositionarea-fraction
In the three regular hexagons shown, X, Y and Z are (in this order) the areas of the grey shaded parts. Which statement is true?
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Answer: A — \(X=Y=Z\)
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Hint 1 of 2
Split each hexagon into six identical small triangles.
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Hint 2 of 2
Count how many of those six equal triangles are shaded in each hexagon.
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Approach: measure each shaded region in sixths of the hexagon
- A regular hexagon divides into six congruent equilateral triangles.
- In each of the three pictures the grey region covers exactly three of those six triangles, i.e. half the hexagon.
- Since the hexagons are the same size, X, Y and Z are all equal.
- So \(X=Y=Z\).
Mark:
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