2006 AMC 12A Problem 6
Attempt Problem 6 of the 2006 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 12A solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
6.
The rectangle is cut into two congruent hexagons, as shown, in such a way that the two hexagons can be repositioned without overlap to form a square. What is
Answer: A
Small hint:
The two hexagons reassemble into a square of area
Big hint:
The staircase splits the width into three equal horizontal pieces that sum to
Solution:
The two hexagons form a square of area so the square has side
The staircase cut splits the width into three equal horizontal pieces of length which together span the full width: so (The two vertical steps each rise building the extra height of the square.)
Thus, the correct answer is A.
Problem 6 in other years
- 1950 AMC 12
- 1951 AMC 12
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