Fun geometry problem

anon_hedgepig

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Want something to do?

Find the area of the shaded region EFGH. Curves are all circular arcs with radius 2, and the quadrilateral is a square.

You shouldn't need to use trig. Algebra and geometry suffice. Feel free to private message me if you want a hint on how to do the problem.
 

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Some hints in order of revealingness:

When I first encountered this problem around a decade ago, there was this hint... Construct triangle EAB.
Method one: look at the three "sided" petal and EFGH "core" region. You can find the area for 2 petals and the "core" as well as 1 petal and the "core". Then, use algebra (basic system of equations) to determine the area.
 
Beer soaked comment follows.

Want something to do?

Find the area of the shaded region EFGH. Curves are all circular arcs with radius 2, and the quadrilateral is a square.

You shouldn't need to use trig. Algebra and geometry suffice. Feel free to private message me if you want a hint on how to do the problem.
Saw it done a few weeks back at YouTube.
 
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