To apply any formula to calculate area of a triangle, one must know the value of at least one angle of the triangle. However, there is one formula for calculating the area of a triangle without measuring any of its angles.
In this article, we will use Heron’s formula, named after the Hero of Alexandria, a Greek mathematician. It takes three lengths (a,b, c) of a triangle and semi-perimeter s. In order to apply this formula, it is mandatory to know the lengths of all three sides of the triangle.
Formula
A = √s (s - a) (s - b) (s - c)
where, a, b and c are the lengths of sides of the triangle where s is half of the perimeter given by s=(a+b+c)/2.
Mathematical illustration
Explanation
While coding, using Heron’s formula is not going to be a challenging task for you if you can compute the square root using a custom or built-in function. Now, let’s have a python program to evaluate the area of a triangle by using the length of the sides.
def calculateArea(a, b, c):
s= (a+b+c)/2 #s is the semi perimeter
area= math.sqrt(s*(s-a)*(s-b)*(s-c))
return area
print(calculateArea (4, 6, 8))
- Line 1: Function definition to calculate the area of a triangle using given sides i.e. a, b, and c.
- Line 2: Calculating the semi perimeter of the triangle by calculating the sum of sides & dividing it by 2.
- Line 3: Computing the area by calculating the square root of the product of
s(s-a)(s-b)(s-c). - Line 4: Returning the area computed by
calculateArea(). - Line 6: Invoking
calculateArea()method with 4, 6, and 8 values for a, b, and c respectively to calculate the area of a triangle.
Output
