Problem 3 · 2017 Math Kangaroo
Medium
Geometry & Measurement
Arithmetic & Operations
areaarea-decomposition
Angelika crafts a piece of jewellery out of two grey and two white stars. The stars have areas of 1 cm², 4 cm², 9 cm² and 16 cm² respectively. She places the stars on top of each other as shown in the diagram and glues them together. How big is the total area of the visible grey parts?
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Answer: B — 10 cm²
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Hint 1 of 2
The stars are stacked biggest at the back, smallest in front.
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Hint 2 of 2
A grey star only shows the ring left after the next (smaller) star covers its middle.
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Approach: subtract each covering star from the grey star beneath it
- Stacked back to front the areas are 16, 9, 4, 1; colours alternate grey, white, grey, white.
- The grey 16-star shows everything except where the white 9-star sits: 16 − 9 = 7.
- The grey 4-star shows everything except the white 1-star on top: 4 − 1 = 3.
- Visible grey = 7 + 3 = 10 cm², choice B.
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