SOLUTION: A area of a equilateral triangle with a side length of {{{8sqrt(3)}}}.

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Question 595991: A area of a equilateral triangle with a side length of 8sqrt%283%29.
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there---
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In order to find the area of a triangle we need to know the base B and the height H. Then we use the formula for the area of a triangle, A=BH/2.
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[I] Find the base
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By definition, the sides of an equilateral triangle are the same, so our base is 8sqrt%283%29.
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[II] Find the height
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If we draw a line segment for the height of the equilateral triangle, we see that it divides the triangle into two congruent 30-60-90 degree right triangles. The hypotenuse of the 30-60-90 triangle is 8sqrt%283%29. Its base is half the length of the hypotenuse, or 4sqrt%283%29, and the height of the other leg is %28sqrt%283%29%29%2F2 times the hypotenuse, or 12.
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[III] Find the area
A=%281%2F2%29%28B%29%28H%29
A=%281%2F2%29%284sqrt%283%29%29%2812%29
A=24sqrt%283%29
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That's it! Feel free to email if any part of the explanation doesn't make sense.
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Mrs.Figgy
math.in.the.vortex@gmail.com