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What is the procedure or methodology of this topic "Investigation New Formula of Area of Arbelos"?
and what is the related literature and related study of this topic?

Please Help me so that I can Defend it on my Proposal Defense this coming January..
I really need help.

Can you give me a new formula of area of an arbelos?

As Mr. Tomlinson recommended a week ago for your same question, are you doing the following experiment?
https://www.sciencebuddies.org/science- ... p012.shtml

If so, then coming up with the formula is the project, and that is what you are going to explore! Have you tried out the java applet they recommend on the project idea page? Have you done other research on arbelos? If so, what have you found?

If you look closely at the shape, do you see familiar shapes in not only the white region but also the surrounding regions? What if you combined the white area and the blue area between the horizontal line and the white region? What shapes do you see?

Good luck!