Problem 3 · 2019 Math Kangaroo
Medium
Geometry & Measurement
areaarea-fractionspatial-reasoning
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Answer: E
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Hint 1 of 2
In most pictures the grey shapes are triangles reaching from the bottom to the top of the rectangle.
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Hint 2 of 2
A triangle spanning the full height has area ½·height·(its base); compare how much total base the grey triangles cover.
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Approach: compare grey area as half times total triangle base
- Every grey triangle spans the full height of the rectangle, so its area is ½·height·(its base).
- In pictures A–D the triangle bases tile the width exactly once, giving grey = ½ of the rectangle.
- In picture E the triangles are packed so their bases overlap and total more than the width, so the grey exceeds half.
- Hence the grey area is largest in (E).
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