1997 AMC 8 Problem 10

Attempt Problem 10 of the 1997 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 1997 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

What fraction of this square region is shaded? Stripes are equal in width, and the figure is drawn to scale.
512\dfrac{5}{12}
12\dfrac{1}{2}
712\dfrac{7}{12}
23\dfrac{2}{3}
56\dfrac{5}{6}
Answer: C
Concepts:area decompositionfraction
Small hint:
Count shaded small squares out of the total
Big hint:
Divide the square into equal small squares matching the stripe widths
Solution:
We can split the square into 62=366^2 = 36 unit squares. The number of shaded small squares is 3+7+11=21. 3 + 7 + 11 = 21.
The fraction of the square that is shaded is 2136=712. \dfrac{21}{36} = \dfrac{7}{12}.
Thus, C is the correct answer.
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