Anequilateral triangleis shown below.

a.) Find an expression for its heighthin terms ofa.

Ok, I have the solution, but I don't understand it. This is how the solutions manual shows it is solved:

step #1: h^2 + (a/2)^2 = a^2

a^2 + b^2 = c^2 Pathagorean formula, ok I understand this.

step #2: h^2 + [(a^2) / 4] = a^2

adivided by 2 squared equalsasquared over 4. Got it.

step #3: h^2 = (3a^2) / 4

Ok this is where I'm lost. Where did the 3 timesasquared come from?

step #4: h = [(3a^2) /4]^(1/2)

I understand this except I still don't know where the 3a^2 came from.hequals the square root of, 3 timesasquared divided by 4.

step #5: h = (a/2)(3^(1/2))

I understand this as well.adivided by 2, times the square root of 3.