SOLUTION: How do you find the area of an equilateral triangle if you only are given the height? The height for my problem is given as 8. Thank you Note: I know the area of a triangle i

Algebra ->  Triangles -> SOLUTION: How do you find the area of an equilateral triangle if you only are given the height? The height for my problem is given as 8. Thank you Note: I know the area of a triangle i      Log On


   

Question 547455: How do you find the area of an equilateral triangle if you only are given the height? The height for my problem is given as 8.
Thank you
Note: I know the area of a triangle is 1/2*Base*height.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Since an equilateral triangle can be constructed using two 30-60-90 triangles, we can find the length of the base (or half the length). The sides of a 30-60-90 triangle are in the ratio 1:sqrt(3):2, and the height 8 corresponds to sqrt(3), so half of the base would be 8/sqrt(3).

To find the area, we can multiply the height (8) by "half the base" (8/sqrt(3)) to get 64/sqrt(3), or 192sqrt(3)/3.

This may sound confusing since I didn't draw or post a diagram, but once you draw an equilateral triangle with the height you'll figure it out!