QUADAREA  Maximal Quadrilateral Area
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.
Input
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.
Output
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.
Example
Input: 2 1 2 1 2 0.5 0.5 0.5 0.5 Output: 2.00 0.25
For the first test case, it is optimal to construct a rectangle, and for the second, a square is optimal.
hide comments
abhisrivastava:
20220917 11:05:23
@dhruv120399 The question says largest possible area...It'll be possible only if the quadrilateral is cyclic. 

mnkp:
20210713 10:05:57
only possible with a specific formula


dhruv120399:
20200331 10:59:12
brahmgupta's formula is only for cyclic quadrilaterals. The question should mention that. 

mrmajumder:
20200321 16:21:38
use fixed with setprecision in cpp 

kundan2000:
20191026 23:00:53
take double as data type for c++


sriharsh_11:
20190111 06:53:37
why isn't setprecision working?


begin_143:
20180930 12:07:33
you need to know brahmgupta formula


masterchef2209:
20180813 10:08:07
brahmagupta's formula like heron's formula for scalene triangle but for quadilaterals


mr_robot_rb01:
20180703 09:21:25
Truncate area to 2 decimal places ...C++ 

vkash:
20180203 07:41:24
cake Walk: 
Added by:  Neal Wu 
Date:  20080524 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO 