Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the regular hexagon be 2 units.
Therefore;
Area regular pentagon is;
5(2.12920428618)²÷(4tan(180/5))
= 7.79980303549 square units.
Area orange is;
Area triangle with side 1.95629520148 units and 1.71576768873 units, and angle 108° + Area triangle with side 2.97412348187 units and 2.09846578712 units, and angle 26.7246503609°
= ½(1.95629520148*1.71576768873)sin108 + ½(2.97412348187*2.09846578712)sin26.7246503609
= 1.59613346963 + 1.4033208553
= 2.99945432493 square units.
Therefore;
Area orange ÷ Area regular pentagon to 2 d. p. is;
2.99945432493 ÷ 7.79980303549
= 0.38455513701
≈ 0.38
