2022 AMC 8 Problem 18
Attempt Problem 18 of the 2022 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 2022 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
18.
The midpoints of the four sides of a rectangle are and What is the area of the rectangle?
Answer: C
Small hint:
The given midpoints form a parallelogram inside the rectangle
Big hint:
The midpoint parallelogram has half the area of the original rectangle
Solution:
The four given midpoints form a parallelogram. Its horizontal base has length , and its height is , so its area is .
For any rectangle, the parallelogram formed by joining the side midpoints has half the area of the rectangle. Therefore the rectangle’s area is .
Thus, the correct answer is C.
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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- 1998 AMC 8
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