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the reason this would take a while for me is that i like to derive the formulas from scratch for such problems...
otherwise i trust not verify, haha.
sometimes being good at math is knowing that someone else derived the formula you need, and knowing where to find that formula.
yes, it's a process... i have the stamina and interest to relearn geometry, because i have a dream to build in stone, make true masonry great again.
i actually ran into a real mason recently. he retired and started making canvas art instead, based on his work as a mason. very intricate, never seen anything like it.
That's a very cool reason to want to learn geometry. I wish you luck in your pursuits!
Nice find, didn't even though there was a formula available for this on Wikipedia
The green area is half a circle segment with height h.
The area of the rectangle is r*(r + r - h).
The area of the semicircle is (pi * r^2) / 2.
Since they are equal, you get h = 2*r - (pi * r)/2
Insert that h into the circular segment area based on height h formula and you get
r ~ 6.3587