2010 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2010 AMC 12B, 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.

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Concepts:area decompositionrectangle

Difficulty rating: 880

2.

A big L is formed as shown. What is its area?

2222

2424

2626

2828

3030

Solution:

The region splits into an 8×28\times2 vertical rectangle and a 2×32\times3 horizontal foot, whose width is 52=3.5-2=3.

The total area is 82+32=16+6=22. 8\cdot2+3\cdot2=16+6=22.

Thus, the correct answer is A.

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