How prove $ \frac{2}{\sqrt3}F \geq s-1 $ for convex quadrilateral?

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Let $Q$ be any convex quadrilateral of area $F$ and semiperimeter $s$.

Suppose that length of any diagonal of $Q$ $ \geq$ length of any side of $Q$ $\geq 1$

How prove $ \frac{2}{\sqrt3}F \geq s-1 $?