First, a circle inscribed in a square looks like this:
If that square has an area of 2, that means each of its sides has a length of √2. And THAT means that the radius of the circle is √2/2.
The area of a circle is πr^2. Plug √2/2 in for r and you’ve got your answer:
from Tumblr https://ift.tt/2vOO5Ll