2017 AMC 8 Problem 18
Attempt Problem 18 of the 2017 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 2017 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
In the non-convex quadrilateral shown below, is a right angle, and What is the area of quadrilateral
Answer: B
Small hint:
First find using the small right triangle.
Big hint:
Then recognize the larger triangle as a -- right triangle and subtract the small triangle’s area.
Video solution:
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Written solution:
Since is a right angle, we can apply the Pythagorean theorem to to get that We also get that is right since the sides of form a Pythagorean triple.
Then the area of is equal to
Thus, B is the correct answer.
Problem 18 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
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
- 2001 AMC 8
- 2002 AMC 8
- 2003 AMC 8
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- 2006 AMC 8
- 2007 AMC 8
- 2008 AMC 8
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- 2012 AMC 8
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- 2026 AMC 8