Problem 8 · 2017 Math Kangaroo
Easy
Geometry & Measurement
area-decomposition
Petra crafts a piece of jewellery out of two black and two white hearts. The hearts have areas of 1 cm², 4 cm², 9 cm² and 16 cm² respectively. She places the hearts on top of each other as shown in the diagram and glues them together. How big is the total area of the visible black parts?
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Answer: B — 10 cm²
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Hint 1 of 2
The hearts are stacked biggest to smallest, with black and white alternating.
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Hint 2 of 2
Visible black = big black minus the white on top, plus the next black, and so on.
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Approach: alternating sum of areas
- Stacking areas 16, 9, 4, 1 with alternating colours, the visible black equals 16 − 9 + 4 − 1.
- That is 16 − 9 + 4 − 1 = 10 cm².
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