# 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 in^{2}.

**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.

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