Find the Perimeter and Area of a regular polygon

[devlin220]

I need to find the perimeter and area of a regular polygon, (an equilateral triangle) but I only have one side length of this triangle and it's 18. I know the perimeter is 18x3, but how do I find the area? I can't use any sort of Trig. I've heard something like the 30,60,90 triangle or something...and that the apothem is square root 3/2, the side is 1/2s and the other side is s. Does this make sense? The answer is 81 times the square root of 3 squared units. I don't know how to get to the answer, though.

 

[Denis]

Sit yourself down, get a pencil, ruler and paper, and draw equilateral triangle ABC:

                   A







  B                D                C

So AB = AC = BC
Draw perpendicular line AD; cuts BC in half: BD = CD
So using your figures, BD = CD = 9.
If you can't find the area now, then you need classroom help: impossible to teach here.

 

[fasteddie65]

There is a special formula for the area of an equilateral triangle.

It is A = s^2 ?3/4, where s = the length of the side.

 

[Denis]

True, FastE, but how will this help the kid in the long-run?
Blindly apply the formula without knowing why it works?
Not realising same formula can be manipulated to find side given area?

I remember lots of "suffering" in High School because our %&*^#$*& math teacher gave us trig tables
(as mysteriously as Father Villeneuve quoted from the &*$%#& you-know-what),
never telling us what they meant or how they were calculated...