Heron's Formula

The area of a triangle can be calculated by using Heron's formula if we only know the length of all three sides of the triangle.

Let's learn more about Heron's formula with a few solved examples.

What Is Heron's Formula?

Heron's formula to calculate the area of the triangle is:

 

 

 

 

 

 

A = √( s(s-a)(s-b)(s-c) )

Where "s" represents the semi-perimeter or half of the perimeter of the triangle and can be calculated as:

s = (a+b+c)/2

a, b, and c are the side lengths of the triangle.  

Solved Examples Using Heron's Formula.

Example1: If the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in. Calculate its area.

Solution: 

To find: Area of the triangle ABC. 

AB  = 4 in, BC = 3 in, AC = 5 in(given)

Using Heron's Formula,

A = √( s(s-a)(s-b)(s-c) )

Finding s,

s = (a+b+c)/2

s = (4+3+5)/2

s = 6

Put the values,

A = √( 6(6-4)(6-3)(6-5) )

A = √( 6(2)(3)(1) )

A =  √( 36) = 6

Answer: The area of the triangle is 6 in².

 

Example 2:

Area of an equilateral triangle is √3 squared unit. Find the length of the sides of the triangle.

Solution:

To find: The length of the sides of the triangle.

Area = √3(given)

Let the length of the triangle is "a" unit. 

Using Heron's Formula,

A = √( s(s-a)(s-b)(s-c) )

Finding s,

s = (a+a+a)/2

s = (3a)/2

Put the values,

A = √( (3a/2)(3a/2-a)(3a/2-a)(3a/2-a) )

A = √( (3a/2)(a/2)(a/2)(a/2) )

A = (a/2)(a/2)√3

Putting the value of A,

√3 =  (a/2)(a/2)√3

a = 2

Answer: The length of the sides of the equilateral triangle is 2 units.