Problem 4 · 2025 Math Kangaroo
Easy
Geometry & Measurement
area-fractiongrid-counting
The regular hexagon shown is divided into a number of triangles of equal area. What fraction of the hexagon is grey?
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Answer: B — 1⁄3
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Hint 1 of 2
Every little triangle in the picture has the same area, so the answer is just (grey triangles) over (all triangles).
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Hint 2 of 2
Count the grey triangles, then count the total, and reduce the fraction.
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Approach: count equal-area triangles, then reduce
- All the small triangles have equal area, so the grey fraction is simply how many are grey out of how many there are.
- The hexagon is cut into 24 equal triangles, and 8 of them are shaded grey.
- So the grey part is \(\frac{8}{24}=\frac{1}{3}\) of the hexagon, which is (B).
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