Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the inscribed regular pentagon be 2 units.
Therefore;
Area green is;
Area rectangle with length 2 units and width 1.17557050458 units.
= 2 * 1.17557050458
= 2.35114100916 square units.
Area red is;
Area regular pentagon with side length 2 units - Area triangle with two side 2 units each, and angle 108° - Area triangle with side 2 units and 0.7639320225 units, and angle 72°
= ((10*2)/(4tan(180/5))) - ½(4)sin108 - ½(2*0.7639320225)sin72
= 6.88190960236 - 1.90211303259 - 0.72654252801
= 4.2532540418 square units.
It implies;
Area green ÷ Area red is;
2.35114100916 ÷ 4.2532540418
= 0.55278640449
≈ 0.55
