A Maximal Inscribed Triangle

The ellipse $E \colon \dfrac{x^2}{4} + y^2 = 1$ has left and right foci $F_1, F_2$. A moving point $P$ on $E$ is such that lines $PF_1$ and $PF_2$ meet $E$ again at points $Q$ and $R$ respectively.

1. When $P$ is the top vertex of $E$, find the area of triangle $PQR$. 2. Prove that the area of triangle $PQR$ is maximized exactly when $P$ is the top or bottom vertex of $E$.