An obtuse triangle is any triangle that is having an obtuse angle which is greater than 90 degrees.
Consider triangle ΔABC:
Its area equals to a difference between area of ΔABD and ΔACD.
The first one equals to
SABD=1/2⋅BD x h
the second one equals to
SACD = 1/2 x CD x h
Their difference equals to
SABC=1/2 x BD x h − 12x CD x h= 12 x (BD−CD) x h=12 x a x h