Let the side length of the congruent square be 1 unit.
Therefore area of the shape is;
8 square unit.
Shaded area is;
Area triangle with two length √(2) units and √(5)/4 units, and angle (135-atan(0.5))°
= ½(√(2)*(√(5)/4))sin(135-atan(0.5))
= 3/8 square units.
Therefore shaded fraction is;
Area shaded or Area blue ÷ Area of the complete shape.
= (3/8) ÷ 8
= 3/64
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