Hero's Formula

Theorem

Fig (i) Fig (ii)

Fig (iii)

Let D = area of triangle

From figure (i), C < 90^o (C is acute) and AD ^ BC.

From figure (ii), C > 90^o (C is obtuse) and AD ^ BC produced.

From figure (iii), C = 90^o.

Alternate form

Note:

Slight manipulation of half anlge formulae lead to the following results.