Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Area BDE is;
Area triangle with side 2 units and 3 units, and angle 120°
= ¼(6√(3))
= ½(3√(3)) square units.
= 2.59807621135 square units.
Area yellow is;
Area triangle with side 2 units and 3 units, and angle 120° - Area triangle with side 2 units and 1.74355957742 units, and angle (60-atan(3√(3)/7))° + Area triangle with side 1.30766968306 units and 3 units, and angle atan(3√(3)/7)° - Area triangle with side 1 unit and 0.41757472899 units, and angle 60°
= ½(3√(3)) - ½(2*1.74355957742)sin(60-atan(3√(3)/7)) + ½(3*1.30766968306)sin(at an(3√(3)/7)) + ½(1*0.375)sin60
= ½(3√(3)) - 0.69282032303 - 1.16913429511 + 0.16237976321
= 0.89850135642 square units.
Therefore;
Area yellow ÷ Area BDE is;
0.89850135642 ÷ 2.59807621135
= 0.34583333333
