Can you find all such quadrilaterals?

Let $ABCD$ be a convex quadrilateral where $E,F,G,H$ are the midpoints of $AB,BC,BD,DA$ respectively.

If $AB+CD=2EG$

$BC+DA=2FH$

define $k =$ $\frac{area \space of \space ABCD}{AB^2+BC^2+CD^2+DA^2}$ .

Then which of the following is true regading $ABCD$ .