2011 AMC 10A Problem 9

Question

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

Find the vertical and horizontal side lengths of the rectangle

The side lengths are

a+b

and

c+d

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.

Problem 9 in other years