Feet of Focal Perpendiculars to a Tangent

Let $O$ be the origin and $F_1,F_2$ the two foci of the ellipse $C:\dfrac{x^2}{4}+y^2=1$. From $F_1$ and $F_2$, perpendiculars are dropped to a tangent line $l$ of the ellipse $C$, with feet $H_1$ and $H_2$ respectively. When $OH_1\perp OH_2$, find the area of $\triangle OH_1H_2$.