# Area of Triangle Using Heron's Formula in PYTHON

Calculate the area of a triangle when all the three sides are known using Heron's Formula in Python.

## Heron's Formula

Hey CodeSpeeder!

Ever got bored of using angles and distances first for calculating the area of a triangle?

Well, thanks to the Hero of Alexandria!

He gave a simple formula to calculate the area of a triangle when all the three sides are known to us.

The formula was named after him as "Heron's Formula".

Look at this figure! All the lengths of the three sides of a triangle a, b, and c are given.

The area A of a triangle is given by:

Here,

a: length of side 1

b: length of side 2

c: length of side 3

s: semi-perimeter of the triangle

A: area of the triangle

## Program

Let's now code a small python implementation for calculating the area of the triangle using Heron's formula!

```import math

# function to calculate the area of a triangle
# when its three sides a, b, and c are given
def areaOfTriangle(a, b, c):
# s is the semi-perimeter of the triangle
s = (a + b + c) / 2
product = s * (s - a) * (s - b) * (s - c)
# product >= means triangle can be formed with the given sides
if product > 0:
# Calculate area using Heron's Formula
area = math.sqrt(product)
# when the triangle can't be formed with the given sides, area=0
else:
area = 0
return area```

## Test-cases and Output

Now let's check the function areaOfTriangle() on various test-cases!

```sides = [(3, 4, 5), (13, 4, 15), (4, 4, 4), (4, 4, 2), (1, 2, 3)]
for (a, b, c) in sides:
print("Area of the triangle with sides a=", a,
"units, b=", b, "units, and c=", c, "units is ",
round(areaOfTriangle(a, b, c), 3),"units^2.")```

Run the above code and you'll get the following output.

```Area of the triangle with sides a= 3 units, b= 4 units, and c= 5 units is  6.0 units^2.
Area of the triangle with sides a= 13 units, b= 4 units, and c= 15 units is  24.0 units^2.
Area of the triangle with sides a= 4 units, b= 4 units, and c= 4 units is  6.928 units^2.
Area of the triangle with sides a= 4 units, b= 4 units, and c= 2 units is  3.873 units^2.
Area of the triangle with sides a= 1 units, b= 2 units, and c= 3 units is  0 units^2.
```

## Fact point!

Look at the test-case 1. It's a right angles triangle with two sides of length 3 and 4 units and a hypotenuse of length 5 units. The area is 6 unit2.

It's the only triangle with consecutive integral side-lengths and area.

## Proof:

Let the consecutive integer sides be d-1, d, d+1 and the area be d+2.

Area using heron's formula A will be

Equating and solving A = d+2.

Submitted by Kalki Pareshkumar Bhavsar (KalkiBhavsar)

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