# Its not a triangle. It's not a sector. It's a Trianglector!

Geometry Level 4

Square $$ABCD$$ has side length $$1$$. The quarter-circle sectors $$BAC$$ and $$ABD$$ are drawn, along with diagonal $$AC$$. If the area of the shaded region is $$\frac{a \pi + b \sqrt{c} + d}{e}$$, where $$a,b,c,d,e$$ are all integers with $$c$$ not divisible by the square of any prime and $$\text{gcd}(a,e) = 1$$, find $$a^2 + b^2 + c^2 + d^2 + e^2$$.

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