Problem 20 · 2025 Math Kangaroo
Medium
Spatial & Visual Reasoning
area-decompositionspatial-reasoning
Elke draws quarter circles on a sheet of paper measuring 12 cm × 9 cm, with the centres at the four corners. She shades the resulting region in the middle of the figure (not drawn to scale). How long is the distance marked with the question mark?
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Answer: B — 6 cm
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Hint 1 of 2
Each quarter circle reaches exactly its radius along the side it starts from, so name the radii and mark where each arc meets the bottom edge.
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Hint 2 of 2
Where two arcs touch, their radii must fit together along that side — use that to pin the radii, then read the marked length off the 12 cm bottom.
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Approach: use the corner-circle radii along the sides
- Each arc reaches its own radius along the edges from its corner; where two arcs meet on the 9 cm right side, those two radii add up to 9.
- Those same radii mark off points along the 12 cm bottom edge, and the question-mark length is what is left between the bottom-left corner and the bottom-right arc.
- Working the radii through the 12 cm width leaves the marked distance equal to 6 cm, which is (B).
Mark:
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