Problem 16 · 2022 Math Kangaroo
Hard
Geometry & Measurement
area-decompositionsymmetry
Gardener Toni plants tulips and sunflowers in a square flowerbed of side length 12 m, as shown. What is the total area where sunflowers are planted?
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Answer: E — 48 m²
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Hint 1 of 2
The flowerbed is a 12 m square; the cuts separating tulips from sunflowers create simple regions.
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Hint 2 of 2
Use the symmetry of the diagram to see that the sunflower area is a fixed fraction of the square.
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Approach: split the square into matching regions
- The square has area 12 x 12 = 144 m squared.
- The drawn cuts divide it so the sunflower regions together make exactly one third of the bed.
- One third of 144 is 48 m squared, so the answer is E.
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