Let a focus of the ellipse \( E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) be \( S(4, 0) \) and its eccentricity be \( \frac{4}{5} \). If the point \( P(3, \alpha) \) lies on \( E \) and \( O \) is the origin, then the area of \( \triangle POS \) is equal to:
