brio-and-his-house-10

Brio wants to get a beautiful house constructed near the National Highway. As his in laws are very much fond of triangles, he decided to give his house a perfect Triangular Shape.
Now, here comes the problem that he faces. The plots in Hackers' Land are all circular in shape. You need to help Brio find the area of the smallest plot that he should buy so as to build his triangular house.

Input:

The first line of the input contains the number of testcases T. Each of the next T lines contain 3 real numbers A, B and C - the dimensions of Brio's House.

Output:

One line per test case containing the area of the plot required upto 4 decimal places.

Constraints:

T ≤ 1000
1 ≤ A , B , C ≤ 1000  

Note : Take pi = 3.1415

SAMPLE INPUT
2
5.0000 3.0000 4.0000
12.0000 13.0000 5.0000


SAMPLE OUTPUT
19.6344
132.7284

Source: hackerearth | Difficulty: EASY
Tags: Fundamentals


Solutions:
#### number of elments input
n = int(input())
#print(n)
pi = 3.1415

for ii in range(n):
	d = input()
	d = d.split()
	a = float(d[0])
	b = float(d[1])
	c = float(d[2])
	#### s = 0.5*(a+b+c)

	s2 = (a+b+c)

	Area = pi*a*a*b*b*c*c/(s2*(s2-2*a)*(s2-2*b)*(s2-2*c))
	print("%.4f"%Area)


from math import sqrt
t=int(eval(input()))
while(t):
	s=input().split()
	a,b,c=float(s[0]),float(s[1]),float(s[2])
	d=sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c))
	r=a*b*c/d
	q=3.1415*r*r
	print(("%.4f" %q))
	t-=1


from decimal import *
from math import sqrt
PI=3.1415
T=int(input())
while T>0:
	A,B,C=list(map(float,input().split(" ")))
	r= (A*B*C)/sqrt((A+B+C)*(B+C-A)*(C+A-B)*(A+B-C))
	a= PI*(r**2)
	print(('%.4f'%(a)))
	T-=1


import math
test=int(eval(input()))
while(test):
	a,b,c=list(map(float,input().split()))
	s=a+b+c
	x=(a*b*c)/(math.sqrt(s*(a+b-c)*(a+c-b)*(b+c-a)))
	area=3.1415*x*x
	print(("%.4f" % (area)))
	test-=1


'''
# Read input from stdin and provide input before running code

name = raw_input('What is your name?\n')
print 'Hi, %s.' % name
'''
PI = 3.1415
for test in range(int(input())):
	a, b, c = list(map(float, input().split()))
	radius = (a * b * c) / (((a+b+c) * (b+c-a) * (c+a-b) * (a+b-c))**0.5)
	area = PI * (radius)**2
	print("%.4f" %(area))


for i in range(eval(input())):
	a, b, c = list(map(float, input().split()))
	S = (a + b + c) / 2
	T = (S * (S-a) * (S-b) * (S-c))**0.5
	r = (a*b*c) / (4*T)
	print('%.4f' % (3.1415 * r**2))


from math import sqrt
for _ in range(int(input())):
	a,b,c = list(map(float,input().split()))
	s=(a+b+c)/2;
	area=sqrt(s*(s-a)*(s-b)*(s-c));
	r=(a*b*c)/(4*area);
	plot=3.1415*r*r;
	print("%.4f"%plot)


PI=3.1415

def f(a,b,c):
	p=(a+b+c)*0.5
	area2=p*(p-a)*(p-b)*(p-c)
	r2=(a*b*c)**2/(16*area2)
	return PI*r2
	
t=int(input())

for i in range(t):
	a,b,c=list(map(float, input().split(" ")))
	print(("{0:.4f}".format(f(a,b,c))))
	


from math import sqrt
t=int(eval(input()))
while(t):
	s=input().split()
	a,b,c=float(s[0]),float(s[1]),float(s[2])
	d=sqrt((a+b+c)*(b+c-a)*(c+a-b)*(a+b-c))
	r=a*b*c/d
	q=3.1415*r*r
	print(("%.4f" %q))
	t-=1


'''
# Read input from stdin and provide input before running code

name = raw_input('What is your name?\n')
print 'Hi, %s.' % name
'''
import math
t=eval(input())
for test in range(t):
	s=input().split(" ")
	a=(float)(s[0])
	b=(float)(s[1])
	c=(float)(s[2])
	num=a*a*b*b*c*c
	denom=(a+b+c)*(b+c-a)*(a+b-c)*(a+c-b)
	x=num/denom
	ans=3.1415*x
	print("%.4f"%(ans))


t=eval(input())
while t>0:
	a,b,c=(float(x) for x in input().split())
	s=(a+b+c)/2
	area=pow((s*(s-a)*(s-b)*(s-c)),0.5)
	r=(a*b*c)/(4*(area))
	print("{:.4f}".format(3.1415*r*r))
	t=t-1


import math
t = int (input())
for i in range(t):
	a = [float(f) for f in input().split()]
	abc = a[0]*a[1]*a[2]
	mul = (a[0]+a[1]+a[2])*(-a[0]+a[1]+a[2])*(a[0]-a[1]+a[2])*(a[0]+a[1]-a[2])
	mulsq = math.sqrt(mul)
	r = abc/mulsq
	x = round(3.1415*r*r,4)
	x =str(x)
	n = x.split('.')
	n1 = n[1]
	lent = 4 - len(n1)
	if lent > 0:
		n2 = n1+ '0'*lent
		n3 = n[0]+'.'+n2
	else: n3 = n[0]+'.'+n1
	print (n3)

	


import sys
PI = 3.1415

def f(a, b, c):
	p = (a + b + c) * 0.5
	area2 = p * (p - a) * (p - b) * (p - c)
	r2 = (a * b * c)**2 / (16 * area2)
	return PI * r2

t = int(input())


for _ in range(t):
	a, b, c = list(map(float, input().split()))
	print(("{0:.4f}".format(f(a, b, c))))