Problem 29 · 2010 Math Kangaroo
Stretch
Geometry & Measurement
area-decomposition
The big equilateral triangle consists of 36 small equilateral triangles, each with an area of 1 cm². Determine the area of triangle ABC.
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Answer: A — 11 cm²
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Hint 1 of 2
Each small triangle is 1 cm², so measure ABC in units of small triangles.
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Hint 2 of 2
Subtract the three corner pieces from the whole big triangle.
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Approach: count small triangles inside ABC
- The big triangle holds 36 unit triangles (area 36 cm²).
- Removing the three corner regions that lie outside triangle ABC leaves an area of 11 unit triangles.
- So the area of ABC is 11 cm².
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