2011 AMC 8 Problem 7
Attempt Problem 7 of the 2011 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 2011 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
7.
Each of the following four large congruent squares is subdivided into combinations of congruent triangles or rectangles and is partially shaded. What percent of the total area is partially shaded?
Small hint:
The four shaded pieces combine to exactly one large square.
Big hint:
Express each shaded part as a fraction of one large square.
Solution:
The top left and the bottom right shaded regions are both a quarter of each square. The top right is one-eighth, and the bottom left is three-eighths. Their combined area is
Therefore, the shaded regions combined equal the area of one square, so they are of the total area.
Thus, C is the correct answer.
Problem 7 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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