2018 AMC 8 Problem 4
Attempt Problem 4 of the 2018 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 2018 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
The twelve-sided figure shown has been drawn on graph paper. What is the area of the figure in
Answer: C
Small hint:
Enclose the figure in an easy rectangle or split it into a central square and small triangles.
Big hint:
The slanted parts form four congruent right triangles of area .
Video solution:
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Written solution:
To solve for the area of the figure, we separate the compound shape into parts that are easier to work with, as such:
As is now clear, there is the center square, with smaller shaded triangles surrounding it.
The area of the square is The other triangles each have a base of and a height of so their area is equal to There are of these triangles, so their total area is
Therefore, the total area is
Thus, the correct answer is C.
Problem 4 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
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- 1998 AMC 8
- 1999 AMC 8
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