There are several formulae for calculating
the area of a given triangle . The Greek mathematician Hero of
Alexandria proved the following formula circa 60 BC:
Hero's formula makes it possible to determine the
area of a triangle when only the lengths of the sides are known. In this
formula, , and are the lengths of the sides of the triangle and
is the half-circumference of the triangle. Use Hero's formula to
determine the area of the given triangle, bearing in mind that the
Euclidean distance between two points and , with the co-ordinates
(,) and (,) is
Input
Six lines with the co-ordinates of the
vertices of the triangle : line 1 contains the -co-ordinate of the
vertex , line 2 contains the -co-ordinate of the vertex
, …, line 6 contains the -co-ordinate of the vertex . All
co-ordinates are given as whole numbers.