2019 AMC 8 Problem 4
Attempt Problem 4 of the 2019 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 2019 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
4.
Quadrilateral is a rhombus with perimeter meters. The length of diagonal is meters. What is the area in square meters of rhombus
Answer: D
Small hint:
Each rhombus side is
Big hint:
The diagonals of a rhombus are perpendicular and bisect each other
Video solution:
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Written solution:
We can split the rhombus up into triangles, each of which looks like this.
We know that this is a right triangle, since the diagonals of a rhombus are perpendicular, and we know the hypotenuse is
Using the Pythagorean theorem, we get the other leg to be
This means that the area of the rhombus is Thus, the correct answer is D.
Problem 4 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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