Problema de métodos numéricos (Extracted from Quarteroni's book)

The area A(T) of a triangle T with sides a, b and c, can be computed using
the following formula

$$\begin{align}&A(T) = \sqrt(p(p-a)(p-b)(p-c))\end{align}$$

where p is half the perimeter of T. Show that in the case of strongly deformed
triangles (a ~ b + c), this formula lacks accuracy and check this
experimentally.