Difference between revisions of "2003 AIME II Problems/Problem 14"

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== Problem ==
 
== Problem ==
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Let <math>A = (0,0)</math> and <math>B = (b,2)</math> be points on the coordinate plane. Let <math>ABCDEF</math> be a convex equilateral hexagon such that <math>\angle FAB = 120^\circ,</math> <math>\overline{AB}\parallel \overline{DE},</math> <math>\overline{BC}\parallel \overline{EF,}</math> <math>\overline{CD}\parallel \overline{FA},</math> and the y-coordinates of its vertices are distinct elements of the set <math>\{0,2,4,6,8,10\}.</math> The area of the hexagon can be written in the form <math>m\sqrt {n},</math> where <math>m</math> and <math>n</math> are positive integers and n is not divisible by the square of any prime. Find <math>m + n.</math>
  
 
== Solution ==
 
== Solution ==
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== See also ==
 
== See also ==
* [[2003 AIME II Problems/Problem 13| Previous problem]]
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{{AIME box|year=2003|n=II|num-b=13|num-a=15}}
 
 
* [[2003 AIME II Problems/Problem 15| Next problem]]
 
 
 
* [[2003 AIME II Problems]]
 

Revision as of 13:41, 21 November 2007

Problem

Let $A = (0,0)$ and $B = (b,2)$ be points on the coordinate plane. Let $ABCDEF$ be a convex equilateral hexagon such that $\angle FAB = 120^\circ,$ $\overline{AB}\parallel \overline{DE},$ $\overline{BC}\parallel \overline{EF,}$ $\overline{CD}\parallel \overline{FA},$ and the y-coordinates of its vertices are distinct elements of the set $\{0,2,4,6,8,10\}.$ The area of the hexagon can be written in the form $m\sqrt {n},$ where $m$ and $n$ are positive integers and n is not divisible by the square of any prime. Find $m + n.$

Solution

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See also

2003 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 13
Followed by
Problem 15
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All AIME Problems and Solutions