Strange region

Calculus Level 4

What is the area of the region defined by the following set of inequalities?

(1)0<2xy<1(2)0<x+y2<1\displaystyle \begin{array}{cc} (1)&0 < 2xy < 1 \\ (2)&0 < \frac{x+y}{2} < 1 \end{array}

If the area is AA, give 100A\left\lfloor100A\right\rfloor.

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