2015 AMC 8 Problem 2
Attempt Problem 2 of the 2015 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
2.
Point is the center of the regular octagon and is the midpoint of the side What fraction of the area of the octagon is shaded?
Answer: D
Small hint:
Draw segments from to every vertex of the octagon.
Big hint:
The shaded region contains three full central triangles and half of another.
Video solution:
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Written solution:
First notice that there are equally sized triangles that can be created with and any two consecutive points. Therefore, they each take up of the total area of the octagon.
The shaded area has three complete triangles and half of the triangle Therefore, the shaded area is of the total area of the octagon.
Thus, the correct answer is D .
Problem 2 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
- 1995 AMC 8
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- 1998 AMC 8
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