2011 AMC 10A Problem 9

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?

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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.

Concepts: coordinate geometry · rectangle · distributive property

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.