Problem 14 · 2016 Math Kangaroo
Stretch
Geometry & Measurement
area-decomposition
What percentage of the area of the triangle is coloured in grey in the adjacent diagram?
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Answer: C — 88%
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Hint 1 of 3
Each side of the big triangle is split into 1 + 3 + 1 = 5 equal parts.
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Hint 2 of 3
Each small white corner triangle has the same angles as the big one, so it is a scaled copy.
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Hint 3 of 3
A shape scaled by a length factor of 1/5 has area (1/5)² of the original.
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Approach: the white corners are scale-1/5 copies
- Every side of the big triangle reads 1 + 3 + 1 = 5, so each side has length 5 in these units.
- Each white corner triangle shares the big triangle's angles and has its two cut-off sides equal to 1, so it is the big triangle shrunk by a factor of 1/5.
- Its area is therefore (1/5)² = 1/25 = 4% of the whole, and the three corners remove 3×4% = 12%.
- The grey region is the rest: 100% − 12% = 88%.
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