Difference between revisions of "2006 AMC 12B Problems/Problem 16"
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Revision as of 09:46, 4 July 2013
Problem
Regular hexagon 
has vertices 
and 
at 
and 
, respectively. What is its area?
Solution
To find the area of the regular hexagon, we only need to calculate the side length.
Drawing in points , 
, and , and connecting and with an auxiliary line, we see two 30-60-90 triangles are formed.
Points and are a distance of 
apart. Half of this distance is the length of the longer leg of the right triangles. Therefore, the side length of the hexagon is 
.
The apothem is thus 
, yielding an area of 
.
See also
| 2006 AMC 12B (Problems • Answer Key • Resources) | |
| 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 | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
