# Heron's formula states the area of a triangle is given 
# by the square root of the product s(s−a)(s−b)(s−c) 
# where a, b and c are the lengths of the sides of the 
# triangle and s=(a+b+c)/2 is the semi-perimeter of the triangle. 

# Compute the area of a triangle (using Heron's formula),
# given its vertices.

###################################################
# Header
print('--------------------------------')
print("       Heron's Formula")
print('--------------------------------')
print('')


###################################################
# Input

print('Supply the coordinates (x1, y1) of the first vertex:')
x1 = input('x1 = ')
y1 = input('y1 = ')
print('Supply the coordinates (x2, y2) of the second vertex:')
x2 = input('x2 = ')
y2 = input('y2 = ')
print('Supply the coordinates (x3, y3) of the third vertex:')
x3 = input('x3 = ')
y3 = input('y3 = ')


###################################################
# Triangle area (Heron's) formula
# Student should enter formulas on the next lines.
# Define and calculate a, b, c, s and area
import math
a = math.sqrt((x2-x1)**2 + (y2-y1)**2)
b = math.sqrt((x3-x2)**2 + (y3-y2)**2)
c = math.sqrt((x1-x3)**2 + (y1-y3)**2)
s = ((a+b+c)/2)
area = math.sqrt(s*(s-a)*(s-b)*(s-c)) 
###################################################
# Output

print('')
print('A triangle with vertices (' + str(x1) + ',' + str(y1) + '),'),
print('(' + str(x2) + ',' + str(y2) + '), and'),
print('(' + str(x3) + ','+ str(y3) + ') has an area of '+ str(area) + '.')


###################################################
# Expected output:
#A triangle with vertices (0,0), (3,4), and (1,1) has an area of 0.5.
#A triangle with vertices (-2,4), (1,6), and (2,1) has an area of 8.5.
#A triangle with vertices (10,0), (0,0), and (0,10) has an area of 50.