1994 AMC 8 Problem 19
Attempt Problem 19 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.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
Around the outside of a by square, construct four semicircles with the four sides of the square as their diameters. Another square, has its sides parallel to the corresponding sides of the original square, and each side of is tangent to one of the semicircles. The area of the square is
Answer: E
Small hint:
Each semicircle has a side of the by square as its diameter, so its radius is
Big hint:
A side of equals the original side length plus two radii
Solution:
Each semicircle is built on a side of length so its radius is A semicircle bulges out from the middle of each side by that radius.
Each side of is the original side plus two radii: So the area of is
Thus, the correct answer is E .
Problem 19 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
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