Question 547465: How do I find the area of an equilateral triangle if I am only given the height? The height (in this case) is 16.
Thank you
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Given it is an equilateral triangle, then a line bisecting any vertex will bisect the opposite side.
This will create two congruent triangles, each of which will be a 30-60-90 triangle.
Recall an equilateral triangle has 3 60-degree angles.
The sides of a 30-60-90 triangle are known to have specific relationships.
The hypotenuse = 2 * the short side, which = 1/2 the base in this case.
The altitude = sqrt(3) * the short side
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We are told the height (altitude) = 16, so.
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sqrt(3)*b/2 = 16
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b = 32/sqrt(3)
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b = 18.47520861406803.
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Check using the Pythagorean theorem.
b/2 = 9.237604307034013
(b/2)^2 = 85.33333333333336
a^2 = 256
c = sqrt(85.33333333333336+256)
c = 18.47520861406803
So, the hypotenuse = 18.47520861406803, which = the base.
Recall, it is an equilateral triangle, so this makes perfect sense.
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Done.
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