Divide trapezoid into 4 equal parts.

Only thing figured out is that each part will have an area of:$$\frac{3*a*a}{8}$$ [If we take side of the square as $a$]

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Hint: use the same shape halving all lenghts (so sides are $\frac12a,\frac12a,a,\frac12\sqrt2a$). Can you fix them in the original figure?