Question 184845: Find the area of an equilateral triangle with a height of 6 square root 3.
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! h=6sqrt(3)
The altitude divides the triangle into 2 equal right triangles.
Each right triangle has angels of 90, 60, and 30 degrees.
The sides are in the ratio of base 1, hopotenuse 2 and height sqrt(3). (SAT question frequently)
In our case the base is 6*1, hypotenuse 6*2 and height 6sqrt(3) or 6, 12, 6sqrt(3).
A=.5hb
=.5*6sqrt(3)*6
=18sqrt(3)
So for the entire equilateral triangle we double the area of the right triangle.
36sqrt(3) Answer
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Ed
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