SOLUTION: what is the area of equilateral triangle if the height of it is 6?

Question 617544: what is the area of equilateral triangle if the height of it is 6?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the area of equilateral triangle if the height of it is 6?
let 2x=length of sides
Draw a perpendicular line from apex to base which cuts triangle in half and gives you a right triangle with legs 6 and x and hypotenuse=2x
By the Pythagorean Theorem:
6=√[(2x)^2-x^2)]=√[4x^2-x^2]=√3x^2=x√3
x=6/√3
2x=12/√3
Area=1/2*base*height=1/2*2x*6=1/2*12/√3*6=36/√3≈20.78 sq units

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