Art of Problem Solving
During AMC 10A/12A testing, the AoPS Wiki is in read-only mode and no edits can be made.

2013 AMC 12B Problems/Problem 16: Difference between revisions

Zverevab (talk | contribs)
Created page with "==Problem== Rhombus <math>ABCD</math> has side length <math>2</math> and <math>\angle B = 120^{\circ}</math>. Region <math>R</math> consists of all points inside of the rhombus ..."
 
Aplus95 (talk | contribs)
No edit summary
Line 4: Line 4:


<math>\textbf{(A)}\ \frac{\sqrt{3}}{3} \qquad \textbf{(B)}\ \frac{\sqrt{3}}{2} \qquad \textbf{(C)}\ \frac{2\sqrt{3}}{3} \qquad \textbf{(D)}\ 1 + \frac{\sqrt{3}}{3} \qquad \textbf{(E)}\ 2</math>
<math>\textbf{(A)}\ \frac{\sqrt{3}}{3} \qquad \textbf{(B)}\ \frac{\sqrt{3}}{2} \qquad \textbf{(C)}\ \frac{2\sqrt{3}}{3} \qquad \textbf{(D)}\ 1 + \frac{\sqrt{3}}{3} \qquad \textbf{(E)}\ 2</math>
==Solution==
== See also ==
{{AMC12 box|year=2013|ab=B|num-b=15|num-a=17}}

Revision as of 17:07, 22 February 2013

Problem

Rhombus $ABCD$ has side length $2$ and $\angle B = 120^{\circ}$. Region $R$ consists of all points inside of the rhombus that are closer to vertex $B$ than any of the other three vertices. What is the area of $R$?

$\textbf{(A)}\ \frac{\sqrt{3}}{3} \qquad \textbf{(B)}\ \frac{\sqrt{3}}{2} \qquad \textbf{(C)}\ \frac{2\sqrt{3}}{3} \qquad \textbf{(D)}\ 1 + \frac{\sqrt{3}}{3} \qquad \textbf{(E)}\ 2$

Solution

See also

2013 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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