First, a circle inscribed in a square looks like this:

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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

The area of a circle is πr^2. Plug √2/2 in for r and you’ve got your answer:

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from Tumblr https://ift.tt/2vOO5Ll