Question

What is the area formula of an obtuse triangle?

Answer 1

The area of ANY triangle equals to half of a product of its base by its altitude. That includes triangles with an obtuse angle.
See below.

Explanation:

Consider triangle `Delta ABC`:

Its area equals to a difference between area of `Delta ABD` and `Delta ACD`.
The first one equals to
`S_(ABD) = 1/2*BD*h`
The second one equals to
`S_(ACD) = 1/2*CD*h`

Their difference equals to
`S_(ABC) = 1/2*BD*h - 1/2*CD*h =`
`= 1/2*(BD-CD)*h = 1/2*a*h`

As you see, the formula is exactly as for a triangle with all acute angles.