The first statement is true. Reasoning below.
= = =
We want to find the area of a fixed circle, so we can throw out the last option. If [tex]r[/tex] changes at all, then so does the area of the circle.
For [tex]s[/tex] to increase would require using a circumscribed polygon with less sides. Again, the circle is fixed, so only a certain length [tex]s[/tex] can fit inside the circle. This eliminates the third option.
Note that if we use a regular hexagon, then [tex]s=r[/tex] automatically, because the component triangles that make up the hexagon are equilateral. Increasing [tex]h[/tex] would require that we use a polygon with more sides, which would simultaneously make [tex]s[/tex] stray away from [tex]r[/tex]. In other words, if [tex]h[/tex] increases, then [tex]s[/tex] decreases, so we can never eventually have [tex]s\to r[/tex] ([tex]r[/tex] is fixed).
That leaves the first option. Indeed, as [tex]n[/tex] increases, we get a polygon that looks increasingly rounder and more like a perfect circle. At the same time, that means [tex]h[/tex] gets larger, but would be bounded above by the circle's perimeter. So as [tex]h[/tex] increases indefinitely, it will eventually "be equal" (in the limit sense) to [tex]r[/tex], so that [tex]rh\to r^2[/tex].
