Whats the formula for the area of a triangle, when you don't know the height?

If you know two sides (sides a and b) and the included angle (∠C), use this formula:  

          Area  =  ½·a·b·sin(C).

If you know the three sides (sides a, b, and c),

first find the semiperimeter (s) by using this formula:  s  =  (a + b + c) / 2

then use Heron's formula:

          Area  =  √[ s·(s - a)·(s - b)·(s - c) ]