SOLUTION: 5)Find the area of a regular hexagon with side 22.

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Question 973416: 5)Find the area of a regular hexagon with side 22.
Found 2 solutions by macston, Boreal:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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A=area; a=length of side=22
For a regular hexagon:
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A=%28%283sqrt%283%29%29%2F2%29a%5E2
A=%28%283sqrt%283%29%29%2F2%2922%5E2
A=%28%283sqrt%283%29%29%2F2%29484
A=%282.6%29484
A=1257.5units%5E2

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
A= (1/2)* perimeter * apothem.
Think of this as 6 isosceles triangles with base 22, and half the base is 11.
Each of the two right triangles within the isosceles triangle has apothem (s/2)*sqrt(3), because the interior angles of a hexagon are 60 degrees, and half of 60 is 30. They are 30-60-90- triangles.
11sqrt(3) is the apothem.
The area of one triangle is (1/2) bh= 11*11sqrt(3)= 121 sqrt (3)
There are 6 such triangles, so the area is 726 *sqrt (3)
Going back to the formula above:
Perimeter is 132, apothem is 11 sqrt (3)
A=(1/2)*132*11 (sqrt (3))=726 sqrt (3) units, or 1257.47 square units.