Let $AB$ be the latus rectum of the parabola $y^2 = 4ax$ in the $xy$-plane. Let $T$ be the region bounded by the finite arc $AB$ of the parabola and the line segment $AB$. A rectangle $PQRS$ of maximum possible area is inscribed in $T$ with $P, Q$ on line $AB$, and $R, S$ on arc $AB$. Then $\frac{\text{area}(PQRS)}{\text{area}(T)}$ equals