Finding area of triangles

Question

In a triangle, the average of any two sides is $6 cm$ more than half of the third side , then find the area of the triangle (in$\ cm ^ {2}$)

Answer 1

Since you asked for a hint, I'll give a big one:

If $a,b,c$ are the side lengths, then Heron's formula says $$A=\sqrt{\frac{a+b+c}2\cdot\color{red}{\frac{a+b-c}2}\cdot\color{red}{\frac{-a+b+c}2}\cdot\color{red}{\frac{a-b+c}2}}$$

The red factors are precisely the average of two sides minus half the third one.

Now... What's the sum of the three red factors?