An Interesting proof in Triangles with Complex Algebra

Heron’s Formula: A brief Introduction

Heron’s Formula is an equation that tells you the area of a triangle provided the lengths of the sides of the triangle are known. Using the traditional formula for area = 1/2*base*height can be a bit tricky because in most cases other than right triangles, you need to find the height of the triangle yourself, which can be a tricky task if you do not know trigonometry.

Heron’s Formula
The semi-perimeter of a triangle is the half of the perimeter

The Derivation

When we derive the equation, we shall make use of the following diagram.

Some Important Points

Once Again I have placed some markers in the form of numbers in superscript to highlight points that need to be taken care of. Here I shall explain them.

The area vector is taken normally outward to the surface under consideration. Here S is the area vector.

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