Difference between revisions of "2006 AMC 12B Problems/Problem 16"
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== Solution 2 == | == Solution 2 == | ||
| − | Solution 2 has the exact same solution as | + | Solution 2 has the exact same solution as Solution 1 denoted, but instead, we do not need to know the value of the apothem. We could just apply s, which is the side length in this very problem, <math>\frac{5\sqrt{6}}{3}</math> into the hexagon area formula, <math>\frac{3 (5 \sqrt{2} )^2 \sqrt{3} }{2}=25\sqrt{3}</math> |
== See also == | == See also == | ||
{{AMC12 box|year=2006|ab=B|num-b=15|num-a=17}} | {{AMC12 box|year=2006|ab=B|num-b=15|num-a=17}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 18:05, 16 August 2021
Contents
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.
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 
.
Solution 2
Solution 2 has the exact same solution as Solution 1 denoted, but instead, we do not need to know the value of the apothem. We could just apply s, which is the side length in this very problem, 
into the hexagon area formula, 
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. 
