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2019 Math Kangaroo

Problem 9

Problem 9 · 2019 Math Kangaroo Medium
Spatial & Visual Reasoning areaarea-decomposition
Figure for Math Kangaroo 2019 Problem 9
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Answer: A
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Hint 1 of 2
Each black region is made of triangles in the unit square — estimate each total area.
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Hint 2 of 2
A triangle is ½·base·height; many thin spikes still cover less than half the square.
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Approach: compare total black areas
  1. In the thin-spike pictures the triangles share the full height but their bases add to less than the full width, keeping the area below ½.
  2. The remaining option fills the largest share of the unit square.
  3. The biggest black area is option A.
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