2013
11-10

Pyramids

Recently in Farland, a country in Asia, a famous scientist Mr. Log Archeo has discovered ancient pyramids. But unlike those in Egypt and Central America, they have triangular (not rectangular) foundation. That is, they are tetrahedrons in mathematical sense. In order to find out some important facts about the early society of the country (it is widely believed that the pyramid sizes are in tight connection with Farland ancient calendar), Mr. Archeo needs to know the volume of the pyramids. Unluckily, he has reliable data about their edge lengths only. Please, help him!

The file contains six positive integer numbers not exceeding 1000 separated by spaces, each number is one of the edge lengths of the pyramid ABCD. The order of the edges is the following: AB, AC, AD, BC, BD, CD.

A real number — the volume printed accurate to four digits after decimal point.

1000 1000 1000 3 4 5

1999.9938

//* @author:
import java.util.*;

public class Main {
static double area( double l1, double l2, double l3 )
{
double p = ( l1 + l2 + l3 ) / 2;
return Math.sqrt( p * (p-l1) * (p-l2) * (p-l3) );
}

static double sq( double a )
{
return a * a;
}

static public void main( String [] str ) throws Exception{
Scanner sc = new Scanner(System.in);
double ab,ad,ac,bc,bd,cd,ah,dh,af,sabc,sbcd, hi, v, bh1, bh2;
ab=sc.nextDouble();
ac=sc.nextDouble();
bc=sc.nextDouble();
bd=sc.nextDouble();
cd=sc.nextDouble();

sabc = area( ab, bc, ac );
sbcd = area( bc, cd, bd );

ah = sabc * 2 / bc;
dh = sbcd * 2 / bc;

bh1 = Math.sqrt( bd*bd - dh*dh );
if( cd*cd > bd*bd + bc*bc ) bh1 = -bh1;

bh2 = Math.sqrt( ab*ab - ah*ah );
if( ac*ac > ab*ab + bc*bc ) bh2 = -bh2;

}