Suppose that the sides of a triangle ABC  that is the lengths a, b and c  are given. We can use the cosine rule to derive
For the area we have the formula 

Along with this we know that for a rightangled triangle with sides x, y and z and rightangle at Z
This relationship holds more generally, for in the case of an obtuse angle then so we have 

whether the angle be acute (or rightangled) or obtuse, since on squaring the sign distinction disappears. Hence for our angle A we have
whether theta be acute or obtuse, so The numerator in the square root is a difference of squares, so we have . Let now . (where s is the socalled semiperimeter) so that the formula finally reaches the form . We have found Hero's Formula which will evaluate the area of a triangle given the lengths of its sides! 