Problem 6 · 2011 Math Kangaroo
Medium
Geometry & Measurement
area-fractionsquare-area
In the picture we can see three squares. The corners of the middle square are on the midpoints of the sides of the larger square, and the corners of the smaller square are on the midpoints of the sides of the middle square. The area of the small square is 6 cm². What is the area of the big square?
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Answer: A — 24 cm²
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Hint 1 of 2
A square drawn on the midpoints of another square has a fixed fraction of its area.
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Hint 2 of 2
Each step outward doubles the area, so apply that twice from the small square.
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Approach: each inner square has half the area of the next one out
- Connecting the midpoints of a square makes a new square with half the area.
- So going outward, the area doubles each step.
- Small = 6, middle = 12, big = 24 cm².
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