SOLUTION: make a regular hexagon of sides as you wish and divide them into six equilateral triangles and find its area ?

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Question 196955: make a regular hexagon of sides as you wish and divide them into six equilateral triangles and find its area ?
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We draw the hexagon:
--->
The interior angles in the center measure 60 deg. => 360%5Eo%2F6=60%5Eo

Being Equilateral, all interior angles are 60 deg.

Let us isolate 1 Triangle:


As you can see, we make all sides equal to 2 units.

Woking Eqn, A%5BT%5D=%281%2F2%29%28b%29%28h%29,wheresystem%28b=%281%2F2%29%282%29=red%281%29%29

Solving "h" via Pyth Theorem:
2%5E2=b%5E2%2Bh%5E2
h%5E2=2%5E2-b%5E2=2%5E2-1%5E1=4-1
red%28h=sqrt%283%29%29

Going Back Working Eqn:
A%5BT%5D=%281%2F2%29%281%29%28sqrt%283%29%29
A%5BT%5D=%281%2F2%29%28sqrt%283%29%29, sq.units
And there are 2 Right Triangles for 1 Equilateral Triangle. Therefore,
2%28A%5BT%5D%29=cross%282%29%2A%281%2Fcross%282%29%29%28sqrt%283%29%29
red%28sqrt%283%29%29 ----> There are 6 Equilateral Triangles:

highlight%28red%28%286%29%28sqrt%283%29%29%29%29 sq.units (Answer)


We can also do it by Trigo function since we know the interior angles.
---> sin60%5Eo=opp%2Fhyp=h%2F2
h=%28sin60%5Eo%29%282%29
red%28h=sqrt%283%29%29
Or, cos60%5Eo=adj%2Fhyp=b%2F2
b=%28cos60%5Eo%29%282%29=0.50%282%29
red%28b=1%29

Just do the same we did for Area of Triangle above.

Thank you,
Jojo