Find the area of the shaded region (inkyvoyd's variation of "FoolForMath's problem(s) of the day)
There's multiple ways to solve this. Anyone who has learned geometry should be capable of solving it, but it is not a particularly easy question. Have fun!

Question

Find the area of the shaded region (inkyvoyd's variation of "FoolForMath's problem(s) of the day)
There's multiple ways to solve this. Anyone who has learned geometry should be capable of solving it, but it is not a particularly easy question. Have fun!

inkyvoyd · Answer

attachment

inkyvoyd · Answer

Other notes: Arcs are circular with radii of 2, and the largest polygon is a square with a side length of two.

inkyvoyd · Answer

Hint: Equilateral triangle.

inkyvoyd · Answer

By the way, I have many more where these came from. I quite literally have 4 or 5 books of math problems in which 10% of them are challenging (this one's especially hard though).

kinggeorge · Answer

Can I have the titles of some of those books that you have?

inkyvoyd · Answer

They are in Chinese. I can assure you that I know how to do this problem, if you want proof, just ask.

kinggeorge · Answer

I just wanted the books myself. But I can't understand Chinese, so....

inkyvoyd · Answer

Well, in that case, I'll try my best to scan a few onto open study every day...

perl · Answer

do you have detailed solutions?

perl · Answer

in english or hindi

inkyvoyd · Answer

I can show you 2 different solutions.

perl · Answer

show me one

inkyvoyd · Answer

I'll put the general solution in a message.

anonymous · Answer

"evilasianmath" ?  lol

inkyvoyd · Answer

lol.

dumbcow · Answer

I found the area to be 0.6942
i used calculus though :|

dumbcow · Answer

|dw:1333534070710:dw|
given :
a+b = pi
x+2a+b = 4

find area of region a by integrating over difference between 2 circles from 0 to 1
$$a = \int\limits_{0}^{1}\sqrt{4-x^{2}}-\sqrt{4-(x-2)^{2}} dx = \sqrt{3}-\pi/3 = 0.685$$
then 
b = pi - a = 2.456
x = .1735

Area of shaded region is 4*x --> 0.6942