First, a circle inscribed in a square looks like this:
![image](https://i0.wp.com/78.media.tumblr.com/f40c357cd47850010be1cf203dc9531d/tumblr_inline_pd4emyGmyc1qio24w_540.png?w=852&ssl=1)
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.
![image](https://i0.wp.com/78.media.tumblr.com/5a7e38c5354b20a06a52467ff04ab729/tumblr_inline_pd4eq3QwA01qio24w_540.png?w=852&ssl=1)
The area of a circle is πr^2. Plug √2/2 in for r and you’ve got your answer:
![image](https://i0.wp.com/78.media.tumblr.com/48f391950028aada6fd29eac088a71ac/tumblr_inline_pd4etkBe0D1qio24w_540.png?w=852&ssl=1)
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