Difference between revisions of "2006 AIME I Problems/Problem 1"
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== Problem == | == Problem == | ||
| − | In | + | In convex hexagon <math>ABCDEF</math>, all six sides are congruent, <math>\angle A</math> and <math>\angle D</math> are right angles, and <math>\angle B, \angle C, \angle E,</math> and <math>\angle F</math> are congruent. The area of the hexagonal region is <math>2116(\sqrt{2}+1).</math> Find <math>AB</math>. |
== Solution == | == Solution == | ||
Revision as of 13:53, 25 September 2007
Problem
In convex hexagon 
, all six sides are congruent, 
and 
are right angles, and 
and 
are congruent. The area of the hexagonal region is 
Find 
.
Solution
From the problem statement, we construct the following diagram:
Using the Pythagorean Theorem:
Substituting 
for 
:
Plugging in the given information:
So the perimeter is 
, and the answer is 
.
See also
| 2006 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
