QUADAREA - Maximal Quadrilateral Area

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You are trying to build a house, but unfortunately you currently have only four available walls with side lengths a, b, c, and d. You want your house to be as big as possible, so you would like to know the largest possible area of any quadrilateral you can construct with these four side lengths.


The first line contains the integer T (1 ≤ T ≤ 2,000), the number of tests. Each test contains a single line with four real numbers: a, b, c, and d (0 < a, b, c, d < 1,000). Note that it will always be possible to form a valid quadrilateral with these lengths; that is, the sum of any three side lengths will be strictly larger than the other one.


For each test case, print a single line containing the largest possible area. Your output will be accepted if it is within 0.01 of the official answer.


1 2 1 2
0.5 0.5 0.5 0.5


For the first test case, it is optimal to construct a rectangle, and for the second, a square is optimal.

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Divyansh Shukla: 2015-10-22 14:11:51

@gohanssj9 This problem uses Bretschneider's formula, using which we can conclude that to maximise the area, the quadrilateral must be cyclic, i.e. sum of two opposite angles must be 180

praveenpourush: 2015-10-11 08:15:30

@gohanssj9 Actually when its asked that the quad area must be maximum so it indirectly means that the quad is CYCLIC!

Last edit: 2015-10-11 08:18:18
alexbandeira: 2015-09-26 18:17:57

Tnk's The Champ! In C does not work with float. Use double with "%lf " at the entrance and "% .2lf " in output.

sonupmandal: 2015-09-23 09:08:09

formula based...!!!

Mohd Ausaf Jafri: 2015-08-13 21:13:44

move it to tutorial ;)

NEO: 2015-07-12 12:42:48

for a given perimeter or length ... circle has the maximum area .... so whenever asked for the maximum area ... consider it as a circle..

karthik1997: 2015-07-11 18:53:05

pure maths
ac in .0.00s
area=sqrt(s-a*s-b*s-c*s-d) ;
yoo brahmagupta

karthik1997: 2015-07-11 18:53:03

pure maths
ac in .0.00s
area=sqrt(s-a*s-b*s-c*s-d) ;
yoo brahmagupta

vasayashwanth: 2015-07-04 08:56:56

no logic at alll.....just a formula........not interesting

Ankush : 2015-06-08 08:42:41

Brahmagupta \m/

Added by:Neal Wu
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO