Area of a triangle given three sides - Proof of Heron's formula

It may be of interest of find the area of a triangle given three sides. This methods does not require to know the base and the height of the triangle (the basic definition of finding the area of a triangle), nor an angle in order to use trigonometry to find the area of a triangle.

The type of triangle need not be right angled or any other special type of triangle - it can be of any type. Here though, for simplicity, we used right angled triangles, in the exercises given, to make it easier to use the traditional way of finding the area of a triangle - 1/2 x base x height in order to confirm the Heron’s formula works.

The proof of Heron’s formula is given in a separate worksheet.