SOLUTION: Find the area of an equilateral triangle (regular 3 gon) with the given measurement. 9 inch perimeter Area= what? pllz help! :)

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Question 281471: Find the area of an equilateral triangle (regular 3 gon) with the given measurement.
9 inch perimeter
Area= what?
pllz help! :)
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
What does the fact that the triangle is equilateral tell you?
What does the perimeter of 9 inches tell you?
so we have a triangle with three sides equal to 3.
if we drop a bisecting line from one vertex to the opposite side we form a right triangle with hypotenuse 3 and the base is 1.5.
the missing side (bisecting line) will be the height of the of the triangle
a=1/2 base (1.5) times the height which we can find using the pythagorean theorem or the 30 60 90 triangle features
1.5^2+h^2=3^2
h^2=6.74
h=2.598
which we could have gotten from sqrt(3)*(1.5) a relationship of 30 60 90 triangles
so the height is sqrt(3)*1.5
and the base is 1.5
a=.5*b*h
a=.5*1.5^2*sqrt(3)
or a=.5*1.5*2.598
a=1.95