Heron’s Formula

 

In geometry, Heron's formula gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.

A triangle with sides a, b, and c.


Area of a Triangle from Sides

We can arrive at the calculation of the area of a triangle if we know the lengths of all three sides of the triangle, using heron’s formula 

Let’s use this two step process: 

Step 1: Calculate "s" (half of the triangles perimeter):

 

Step 2: Then calculate the Area:

 
 

Example:

  • What is the area of a triangle where every side is 5 long?

Step 1: s = (5+5+5)/2 = 7.5
Step 2: A = √(7.5 × 2.5 × 2.5 × 2.5) = √(117.1875) = 10.825...