I presume you are talking about problem 16? This will help you out.
-Dan
Hi everyone. I'm a little stuck on how to solve this problem.
2010 AMC 10B Problems - AoPSWiki
Basically, there's a circle and a square with the same center. I can't just take the area of the circle minus the area of the square, since some of the square lies outside of the circle. How do I take that into account?
The answer, by the way, should be "B."
Yes, that's the problem (16) and thanks for the link.
So I played around using those formulas, and also analyzed the circle/square situation further. Apparently the triangle that is below the "circular segment" as depicted by wikipedia is an equilateral triangle, with sides of root3 over 3. Therefore theta = 60 degrees.
By using the formula of wikipedia, and multiplying it by 4 to take into account the 4 circular regions out of the square, I ended up with
Where A should be the answer to the question. But I get...
Something isn't right here ....
Edit: I should have said this before, but pi/3 for the first term represents the area of the entire circle.