SOLUTION: Hello, I am interested in eventually being a tutor initially in geometry, and have been working on this site the last few days under the name Cleomenius. I have come across a

Question 478207: Hello,
I am interested in eventually being a tutor initially in geometry, and have been working on this site the last few days under the name Cleomenius.
I have come across a problem I would like to see if I can get a more clear understanding of.
The problem is, what would be the general formula for the following:
A square is inscribed in a circle.
What would be the general formula for the area of the circle that is not included in the square?
I know the formula for the area of the square and the area of the circle, and we would have to subtract the area of the square from the circle, but cannot seem to produce a general formula that makes any sense to me.
If you can help, I would appreciate it.
Thank you,
Barnabas Kalina.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let side of square = s
Then diag of square = (sqrt(2))s
---
Then radius of circle = (sqrt(2)s)/2
----
Area of circle = (pi)r^2 = (pi)(s^2/2)
Area of square = s^2
----
Area in circle outside square = (pi)(s^2/2) - s^2 = s^2[(pi/2)-1]
=============
Cheers,
Stan H.
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