2014 AMC 8 Problem 6
Attempt Problem 6 of the 2014 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 2014 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
6.
Six rectangles each with a common base width of have lengths of and What is the sum of the areas of the six rectangles?
Small hint:
Each rectangle has area times its listed length.
Big hint:
Add the lengths first, then multiply by .
Solution:
To find the area of each rectangle we multiply by their respective lengths. This means that we can factor out the and we are left with the sum of the lengths. Adding together the lengths, we get
Therefore, the sum of the areas is
Thus, D is the correct answer.
Problem 6 in other years
- 1985 AMC 8
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