Geometry
posted by SkatingDJ .
Find the area of a hexagon with the indicated apothem:
6 sqr root 3
108 sqr root 3 in.^2
432 sqr root 3 in.^2
96 sqr root 3 in.^2
216 sqr root 3 in.^2
Last question, don't know. Please help? Thanks

Geometry 
Reiny
Area = 1/2 x perimeter x apothem
= 1/2 (6s)(6√3)
once you tell me what the side (s) of the hexagon is, we an finish the question 
Geometry 
SkatingDJ
They don't tell you the sides, the apothem is all they give you.

Geometry 
Reiny
So, I guess we can't find the area, since we need the side

Geometry 
SkatingDJ
Hm, I mean, there has to be a way to figure the side out with just the apothem. Problem is that I'm not good with formulas or square roots.
First off, what is the apothem? What is 6 square root 3? 
Geometry 
Reiny
ok, ok
I stand corrected, there is a way, we have an angle.
The apothem is the distance from the centre to the midpoint of a side
Let's look at one of the triangles of the hexagon.
It has a central angle of 60
so in a rightangled triangle formed by the apothem and half the base, I'll call it x
x/6√3 = tan 30
x = 6√3tan30
base = 12√3tan30= 12
area = Area = 1/2 x perimeter x apothem
= (1/2)(72)(6√3)
= 216√3 units^2
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