1991 AMC 8 Problem 10

Attempt Problem 10 of the 1991 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 1991 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

10.

The area in square units of the region enclosed by parallelogram ABCDABCD is
66
88
1212
1515
1818
Answer: B
Concepts:coordinate geometryparallelogramarea
Small hint:
Take BC‾\overline{BC} as the base; it is horizontal from B(0,2)B(0,2) to C(4,2)C(4,2)
Big hint:
The area is base times height, where the height is the vertical distance between the two horizontal sides
Solution:
Side BCBC runs from (0,2)(0,2) to (4,2),(4,2), so the base is 4.4. The opposite side ADAD lies on the xx-axis, so the height is 2.2.
The area is 4×2=8.4 \times 2 = 8.
Thus, the correct answer is B .
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