2012 AMC 8 Problem 23
Attempt Problem 23 of the 2012 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 2012 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
An equilateral triangle and a regular hexagon have equal perimeters. If the triangle’s area is , what is the area of the hexagon?
Answer: C
Small hint:
Equal perimeters make the hexagon side half the triangle side.
Big hint:
A regular hexagon is made from six congruent equilateral triangles.
Video solution:
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Written solution:
Let the side length of the triangle be This means the perimeter is Therefore, the side length for the hexagon is
A hexagon can be made of equilateral triangles with side length as shown above. Each triangle is the original triangle scaled down by so the area is scaled down by Therefore, the area of each of these triangles is Since there are of them, the area is
Thus, the answer is C .
Problem 23 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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