Is the area of an equalateral triangle also base * height/2

I know that the equalateral triangle formula is generally (s^2*sqrt. 3) / 4 but is it also still base * height / 2 or is that just for right triangles?

The "height" of a triangle is the length of the line drawn from the top angle, perpendicular to the "base"

In such a case, then the area of ALL triangles is (1/2) * base * height
even if the height is completely outside the triangle.

In a right-angle triangle, you do not need to draw a separate height, because you already have one side that is perpendicular to another side (use one side as the base, then the other side is the height).

In an equilateral triangle, the height will fall right in the middle of the base. But it will be a line that you have to draw (it is not one of the existing three sides).

---

In this triangle, the height is the line marked "h" while the base is the side marked "b"
http://upload.wikimedia.org/wikipedia/co…

The triangle is not equilateral, but the idea is the same. h starts at the apex and "falls" perpendicular to the base.

Base times height divided by 2 only works for a right angled triangle. It works because if you take 2 identical right angled triangles you get a rectangle which you would calculate the area by multiplying its two sides together so halving it gives the triangle area.

If you're given the height and the base of the equilateral triangle then the equation still holds.

That is for all triangles. Equilaterals are unique in that by knowing just the length of a side you can compute area.

you can still use (base*height)/2 but make sure you use the vertical height and NOT the slant height

Yes the area of all triangle is base times height over 2.

Yes, ½bh works too.