2010 AMC 12B Problem 2

Attempt Problem 2 of the 2010 AMC 12B 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 2010 AMC 12B solutions, or check the answer key.

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

2.

A big L is formed as shown. What is its area?
2222
2424
2626
2828
3030
Answer: A
Concepts:area decompositionrectangle
Small hint:
Split the L into two rectangles
Big hint:
The vertical bar is 2×8,2\times8, and the foot adds a 2×32\times3 piece since 5−2=35-2=3
Solution:
The region splits into an 8×28\times2 vertical rectangle and a 2×32\times3 horizontal foot, whose width is 5−2=3.5-2=3.
The total area is 8⋅2+3⋅2=16+6=22. 8\cdot2+3\cdot2=16+6=22.
Thus, the correct answer is A.
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