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