407173: GYM102697 144 Triangulation Rocks the Nation

You have a triangle with three points given in coordinates. Given this information, figure out the triangle's area. The points can be given in any order.

To calculate the area of a triangle, you can use Heron's Formula, which is described below:

Define $$$A$$$, $$$B$$$, and $$$C$$$ to be the lengths of the three sides of the triangle.

Define $$$S$$$ to be equal to $$$\frac{A + B + C}{2}$$$.

Then, the area of the triangle is calculated as $$$\sqrt{S(S - A)(S - B)(S - C)}$$$.

The input consists of three lines, each consisting of two space-separated integers $$$x$$$ and $$$y$$$: the coordinates of each point of the triangle.

Output a single decimal number $$$a$$$: the area of the triangle, using Heron's Formula as described above. Do not round your answer.

1 1
5 4
2 8

12.5

0 0
8 0
4 8

32.0

-1 -3
2 7
9 -11

62.0

This triangle corresponds to the first example case: