1994 AMC 8 Problem 12
Attempt Problem 12 of the 1994 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 1994 AMC 8 solutions, or check the answer key.
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12.
Each of the three large squares shown is the same size. Segments that intersect the sides of the squares intersect at the midpoints of the sides. How do the shaded areas of these squares compare?
The shaded areas in all three are equal.
Only the shaded areas of and are equal.
Only the shaded areas of and are equal.
Only the shaded areas of and are equal.
The shaded areas of and are all
different.
Answer: A
Small hint:
Find what fraction of each large square is shaded by cutting each figure into equal smaller pieces.
Big hint:
Divide square into equal triangles, square into equal cells, and square into equal triangles, then count the shaded pieces in each.
Solution:
In square of the equal cells is shaded, so of it is shaded.
Square breaks into equal triangles with shaded, and square breaks into equal triangles with shaded; each of these equals
Since every figure has exactly shaded, the shaded areas are all equal.
Thus, the correct answer is A .
Problem 12 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
- 1995 AMC 8
- 1996 AMC 8
- 1997 AMC 8
- 1998 AMC 8
- 1999 AMC 8
- 2000 AMC 8
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