2004 AMC 8 Problem 25
Attempt Problem 25 of the 2004 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 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
25.
Two squares intersect at right angles, bisecting their intersecting sides, as shown. The circle’s diameter is the segment between the two points of intersection. What is the area of the shaded region created by removing the circle from the squares?
Answer: D
Small hint:
Find the area covered by the union of the two squares.
Big hint:
The circle diameter is the diagonal of the overlap square.
Solution:
The two squares have total area but their overlap is a square with area Thus the area covered by the union of the two squares is
The circle’s diameter is the diagonal of that overlap square, so the diameter is and the radius is
The circle area is so the shaded area is
Thus, D is the correct answer.
Problem 25 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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