Let the square side be 2 units.
tan30 = a/2
a = ⅓(2√(3)) unit.
sin60 = 2/b
b = ⅓(4√(3)) units.
c = 2-a
c = ⅓(6-2√(3)) units.
It implies;
Area Shaded is;
2(½*(⅓(6-2√(3)))²sin60) + 2*⅓(6-2√(3))
= ⅓(4√(3)) square units.
Area of the composite shape is;
Area Shaded + 2(½*(⅓(4√(3)))²sin60)
= ⅓(4√(3)) + ⅓(8√(3))
= 4√(3) square units.
Therefore;
Fraction Shaded is;
⅓(4√(3)) ÷ 4√(3)
= ⅓
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