Question 1008228: Find the are of an equilateral triangle of side a.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you can look it up or you can derive it.
if you look it up, you will see that the area of an equilateral triangle = a^2 * sqrt(3) / 4.
you derive it by using pythagorus rule for right triangles and solve for h in terms of a.
you will get h = a * sqrt(3)/2
area of any triangle = 1/2 * b * h which then becomes area of equilateral triangle = 1/2 * a * a * sqrt(3) / 2 which then becomes area of equilateral triangle = a^2 * sqrt(3) / 4.
either way, you will get area of equilateral triangle = a^2 * sqrt(3) / 4.
for example, if you let a = 20, then the area should be equal to 20^2 * sqrt(3) / 4 which would be equal to 100 * sqrt(3)
the height, by pythagorus, would be equal to sqrt(20^2 - 10^2) = sqrt(400-100) = sqrt(300) = sqrt(100*3) = 10*sqrt(3).
you have a height of 10 * sqrt(3) and a base of 20 and a hypotenuse of 20.
area = 1/2 * base * height = 1/2 * 20 * 10 * sqrt(3) which is equal to 100 * sqrt(3).
it checks out, so the formula for area in terma of a must be correct.
area of equilateral triangle = a^2 * sqrt(3) / 4.
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