2011 AMC 10A Problems/Problem 9

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?

$\textbf{(A)}\ ac+ad+bc+bd\qquad\textbf{(B)}\ ac-ad+bc-bd\qquad\textbf{(C)}\ ac+ad-bc-bd   \quad\quad\qquad\textbf{(D)}\ -ac-ad+bc+bd\qquad\textbf{(E)}\ ac-ad-bc+bd$

Solution

We have a rectangle of side lengths $a-(-b)=a+b$ and $d-(-c)=c+d.$ Thus the area of this rectangle is $(a + b)(c + d) = \boxed{\textbf{(A)}\ ac + ad + bc + bd}$.

Video Solution

https://youtu.be/n0qUd4ukEF8

~savannahsolver

See Also

2011 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 8
Followed by
Problem 10
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All AMC 10 Problems and Solutions

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