Let \(P\) be a point inside triangle \(ABC\). Let \(D\), \(E\), and \(F\) be the feet of the perpendiculars from \(P\) to \(BC\), \(CA\), and \(AB\), respectively. Suppose \(AP = 8\), \(BP = 6\), and \(CP = 10\). Find the area of triangle \(ABC\).