Problem 11 · 2018 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellationarea
Tom wants to completely cover his paper boat using the two shapes shown (a small square and a trapezoid). What is the smallest number of shapes he needs?
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Answer: B — 6
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Hint 1 of 2
You want to fill the whole boat with no gaps, so try to use the bigger shape as often as it fits.
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Hint 2 of 2
Cover the wide bottom of the boat with the big pieces first, then patch the corners with the small ones.
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Approach: fill the boat using the big piece wherever it fits, then patch the rest, counting pieces
- Start by laying the bigger shape across the parts of the boat where it fits exactly.
- Fill the leftover corners and edges with the smaller shape so there are no gaps.
- The fewest shapes that cover the whole boat is 6, answer B.
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