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...