\(\Delta ABC\) has side lengths \(4\), \(51\) and \(53\). Each of its sides are trisected and lines are drawn to each point of trisection from their corresponding angle. By doing this, a hexagon is created in the middle of the triangle. The area of this hexagon can be represented by \(p=x(x-1)(x-2)^2+x\) where \(x\) is an integer and \(p\) is the area of the hexagon. Find \(x\).
This problem is similar to one I posted previously but took down. This problem has different lengths and a different solution.