2011 AMC 10A Problem 9

Attempt Problem 9 of the 2011 AMC 10A 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 2011 AMC 10A solutions, or check the answer key.

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

A rectangular region is bounded by the graphs of the equations $y=a, y=-b, x=-c,$ and $x=d,$ where $a,b,c,$ and $d$ are all positive numbers. Which of the following represents the area of this region?

$ac+ad+bc+bd$

$ac-ad+bc-bd$

$ac+ad-bc-bd$

$-ac-ad+bc+bd$

$ac-ad-bc+bd$

Answer: A

Concepts:coordinate geometry rectangle distributive property

Difficulty rating: 900

Solution:

Note that the region is a rectangle with side lengths $a - (-b) = a + b$ and $d - (-c) = c + d.$ The area is then $(a + b)(c + d) =$ $ac + ad + bc + bd.$

Thus, A is the correct answer.

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