Difference between revisions of "2008 AMC 12B Problems/Problem 13"

Revision as of 16:41, 31 May 2011

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Problem

Vertex $E$ of equilateral $\triangle{ABE}$ is in the interior of unit square $ABCD$ . Let $R$ be the region consisting of all points inside $ABCD$ and outside $\triangle{ABC}$ whose distance from $AD$ is between $\frac{1}{3}$ and $\frac{2}{3}$ . What is the area of $R$ ?

$\textbf{(A)}\ \frac{12-5\sqrt3}{72} \qquad \textbf{(B)}\ \frac{12-5\sqrt3}{36} \qquad \textbf{(C)}\ \frac{\sqrt3}{18} \qquad \textbf{(D)}\ \frac{3-\sqrt3}{9} \qquad \textbf{(E)}\ \frac{\sqrt3}{12}$

2008 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 12	Followed by Problem 14
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 12 Problems and Solutions

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 ==Problem==
-Vertex <math>E</math> of equilateral <math>\triangle{ABC}</math> is in the interior of unit square <math>ABCD</math>. Let <math>R</math> be the region consisting of all points inside <math>ABCD</math> and outside <math>\triangle{ABC}</math> whose distance from <math>AD</math> is between <math>\frac{1}{3}</math> and <math>\frac{2}{3}</math>. What is the area of <math>R</math>?
+Vertex <math>E</math> of equilateral <math>\triangle{ABE}</math> is in the interior of unit square <math>ABCD</math>. Let <math>R</math> be the region consisting of all points inside <math>ABCD</math> and outside <math>\triangle{ABC}</math> whose distance from <math>AD</math> is between <math>\frac{1}{3}</math> and <math>\frac{2}{3}</math>. What is the area of <math>R</math>?
 <math>\textbf{(A)}\ \frac{12-5\sqrt3}{72} \qquad

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Difference between revisions of "2008 AMC 12B Problems/Problem 13"

Revision as of 16:41, 31 May 2011

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