Problem 25 · 2017 Math Kangaroo
Stretch
Geometry & Measurement
area-fraction
The diagram shows Maria’s square tablecloth to scale. All small light squares are equally big, and their diagonals are parallel to the sides of the tablecloth. Which part of the whole tablecloth is black?
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Answer: D — 32%
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Hint 1 of 2
The light squares are tilted 45°; split the border into a grid of small equal triangles.
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Hint 2 of 2
Count black triangles against the total to get the black fraction.
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Approach: tile into equal triangles and count
- Because each light square's diagonals line up with the cloth's sides, the whole cloth divides into many congruent small triangles.
- Counting the black triangles against the total gives the black share.
- That fraction works out to 32%.
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