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Question: How to calculate the area of the set

Question:How to calculate the area of the set

Markiyan Hirnyk 7799 Maple 2017
mathematica area intersection
October 22 2017
2 
restart; CodeTools:-Usage(plots:-inequal({abs(abs(x-y)-abs(x+y)) >= 2*y-x+1, (x+1)^2+(y+1)^2 <= 2}, 
optionsimplicit = [gridrefine = 2, rational = true], x = -3 .. 1, y = -3 .. 0., scaling = constrained));

memory used=0.57GiB, alloc change=184.01MiB, cpu time=16.22s, real time=17.24s, gc time=1.58s

?

Mathematica 11.2.0.0 says

113053/146523-8/169 sqrt(22)+32/289 sqrt(30)-3/169 sqrt(214-24 sqrt(22))-
2/169 sqrt(1177-132 sqrt(22))-1/289 sqrt(94-16 sqrt(30))-
4/289 sqrt(705-120 sqrt(30))+1/146523 293046(Pi)-
arcsin(1/13 sqrt(2) (3+sqrt(22)))-arcsin(1/17 sqrt(2) (1+2 sqrt(30)))

(see Area.pdf).
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