2007 AMC 8 Problem 12
Attempt Problem 12 of the 2007 AMC 8 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 2007 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
12.
A unit hexagram is composed of a regular hexagon of side length and its equilateral triangular extensions, as shown in the diagram. What is the ratio of the area of the extensions to the area of the original hexagon?
Answer: A
Small hint:
Divide the regular hexagon into six congruent equilateral triangles.
Big hint:
Each exterior triangle shares a side with one of the six interior triangles.
Solution:
Note that we can split the hexagon into congruent equilateral triangles as follows.
Since each of them share an edge with an exterior triangle, all the triangles are congruent. Therefore, the ratio of areas is
Thus, A is the correct answer.
Problem 12 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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