SOLUTION: What is the altitude of an equilateral triangle with side length of 6 yards. What is the area?

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Question 394352: What is the altitude of an equilateral triangle with side length of 6 yards. What is the area?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
When you draw the altitude, you divide the equilateral triangle into two right
triangles. In one of the right triangles, one of the legs is 3, the other
leg is the altitude, and the hypotenuse is 6.
So you use the Pythagorean+theorem:
let altitude be h
one leg squared plus the other leg squared = the hypotenuse squared.
3+%5E2%2B+a+%5E2+=+6+%5E2
9+%2B+h%5E2=+36

h+%5E2=+27
h+=+sqrt%28+27%29
Which you simplify to 3 times thesqrt%283%29

h+=+3+%2Asqrt%28+3%29

Altitude h+=+5.2+



The area is half the product of base and height.
base a+=+6
h+=+3%2Asqrt%28+3%29

A+=+a%28h%2F2%29
A+=%286%29%283+%2Asqrt%28+3%29%2F2+%29
A+=+3%283%2Asqrt%28+3%29%29
A=+15.59++%29