The points $(4, 0)$ and $(-4, 0)$ are two non-consecutive vertices of a rhombus with an area of $80$ square units. One of the other vertices is $(0, K)$ where $K > 0$. What is the value of $K$?

The area of a rhombus =

(1/2) product of the diagonal lengths

One diagonal length is 8.....so the other must be 20

And the mid-point of this diagonal is at the origin

So.....(0,10) and (0, -10) are the other two vertices

So....K must be 10