Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the regular nonagon be 2 units.
Therefore;
Area purple is;
Area triangle with two equal length 2 units each and angle 140°, the angle they form + Area rectangle with length √(3) units and width 1 unit + Area rectangle with length √(8-8cos140) units and width √(3) units.
= ½(4sin140)+(1*√(3))+(√(3)*√(8-8cos140))
= 9.52800747773 square units.
Area yellow is;
2(area triangle with two lengths √(8-8cos140) units and 1.48445439795 units, and angle 100°, the angle they form)
= 2(½√(8-8cos140)*1.48445439795sin100)
= 5.49495483896 square units.
Area yellow ÷ Area purple to 2 decimal places is;
5.49495483896÷9.52800747773
= 0.57671605021
≈ 0.58
