Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the regular pentagon be 1 unit.
Therefore;
Area purple is;
Area trapezium with two parallel side 0.07294901687 units and 0.38196601125 units, and height cos18 units.
= 0.5*cos18*(0.07294901687+0.38196601125)
= 0.21632495093 space units.
Area yellow is;
Area trapezium with two parallel side 0.27345747199 units and 1 unit, and height 1 unit - Area triangle with height 0.27345747199 units and base 0.198678483 units.
= (0.5*1*(0.27345747199+1)) - (0.5*0.27345747199*0.198678483)
= 0.636728736 - 0.02716505785
= 0.60956367815 space units.
It implies;
Area Purple ÷ Area Yellow to 3 d. p. is;
0.21632495093 ÷ 0.60956367815
= 0.35488490979
≈ 0.355
