how do you find the height of a triangle that is 20cm. on each side

So you have an equilateral triangle with sides 20 cm?

draw in the height, it will right-bisect the base, call the height h
Now look at the right angled triangle with sides
h, 10, and hypotenuse 20
h^2 + 10^2 = 20^2
h^2 = 300
h = √300 or 10√3