2006 AMC 8 Problem 5
Attempt Problem 5 of the 2006 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 2006 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
5.
Points and are midpoints of the sides of the larger square. If the larger square has area what is the area of the smaller square?
Answer: D
Small hint:
The four corner triangles around the smaller square are congruent.
Big hint:
Those four outside triangles can be rearranged to cover the smaller square.
Solution:
Note that we can fold all the triangles in to perfectly cover the smaller square. This means that area of the smaller square is half the area of the larger square.
This makes the area of the smaller square
Thus, D is the correct answer.
Problem 5 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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