Problem 9 · 2025 Math Kangaroo
Easy
Geometry & Measurement
areacomplementary-counting
Five circles, each with an area of 8 cm², overlap to form the figure shown. Each overlapping region has an area of 1 cm². What is the total area of the figure, in cm²?
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Answer: B — 36
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Hint 1 of 2
Add the five circle areas, then fix the double counting where they overlap.
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Hint 2 of 2
Each of the four overlaps was counted twice, so subtract it once.
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Approach: inclusion–exclusion on overlapping areas
- Five circles give 5 × 8 = 40 cm² if simply added.
- The four overlap regions (1 cm² each) were each counted twice, so subtract 4 cm².
- Total figure area = \(40 - 4 = 36\) cm², which is (B).
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