Let the side length of the square be a.
tanb = (0.5a)/a
b = atan(½)°
c = 90-b
c = atan(2)°
sin(atan(2)) = d/a
d = 0.894427191a units.
Calculating a.
(3√(2))² = (0.894427191a)²+a²-2*0.894427191a*acos(atan(2))
18 = 0.8a²+a²-0.8a²
a² = 18 square units.
Where a² is the area of the square.
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