Mathematics teacher and she
Sir Mike Ambrose is the author of the question.
Notice;
The single length of the square is equal the single side length of half the regular hexagon.
Let it be 2 units.
Therefore area square is;
2² = 4 square units.
Area yellow is;
Area square with length 2 units - area triangle with height 2 units and base ⅓(2√(3)) units - area triangle with height 2 units and base ⅔ units - area triangle with side (4/3) units and (4sin(atan⅓))/(3sin(120-atan⅓)) units and angle 60°
= 4 - ½(2*⅓(2√(3)) - ½(2*⅔) - ½((4/3)*(4sin(atan⅓))/(3sin(120-atan⅓))sin60
= 4 - ⅓(2√(3)) - ⅔ - ½(0.43037460745*(4/3))sin60
= ⅓(12-2√(3)-2) - 0.24847689547
= ⅓(10-2√(3)) - 0.24847689547
= 1.93015589948 square units.
It implies;
Area yellow ÷ Area square in its simplest decimal form is;
1.93015589948 ÷ 4
= 0.48253897487
