2020 AMC 8 Problem 18
Attempt Problem 18 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
Rectangle is inscribed in a semicircle with diameter as shown in the figure. Let and let What is the area of
Answer: A
Small hint:
The diameter is
Big hint:
Use the radius and half the rectangle base in a right triangle
Video solution:
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Written solution:
Since is the diameter of the semicircle, we know the length of the diameter is and so the radius is Let be the center of the diameter.
The length from therefore is
Since is on we know
Also, since we have a semicircle, we know
Finally, since is a rectangle, we know is a right angle. This means we can find by the Pythagorean Theorem. We know
Thus, the area of the rectangle is
Thus, the correct answer is A.
Problem 18 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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