Introduction to Scientific Computation Using Python

by Arun Prasaad Gunasekaran

Video 5 : Area of a Triangle using Heron Formula.

Table of Contents

• Introduction to Scientific Computation Using Python
  • Table of Contents
  • Area of a Triangle
  • Interactive animation using Geogebra
  • Program
  • Output

Area of a Triangle

A triangle has many formulae to find its area. One formulae that involves only the sides of the triangle is the Heron’s formula or the Hero’s formula.

If \(a\), \(b\), and \(c\) are the sides of a triangle ABC, then the area of the triangle \(\Delta\) is given by

\[\Delta = \sqrt{s(s-a)(s-b)(s-c)}\]

where \(s = \displaystyle{\frac{a + b + c}{2}}\) is the semi-perimeter of the triangle.

Interactive animation using Geogebra

Program

'''
Program to calculate the area of a triangle using Heron's formulae
'''

# Get inputs
a = float(input("Enter the side 'a' of the triangle:"))
b = float(input("Enter the side 'b' of the triangle:"))
c = float(input("Enter the side 'c' of the triangle:"))

# Calculate the semi-perimeter
s = (a + b + c)*0.5

# Find the Area
Area = (s*(s-a)*(s-b)*(s-c))**0.5

# Print the result
print("The area of the triangle with sides a = {}, b = {}, and c = {} is {}".format(a, b, c, Area))

Output

Enter the side 'a' of the triangle:3
Enter the side 'b' of the triangle:4
Enter the side 'c' of the triangle:5
The area of the triangle with sides a = 3.0, b = 4.0, and c = 5.0 is 6.0