Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the regular pentagon be 1 unit.
It implies;
Area red is;
½*sin54*cos54
= 0.23776412908 square units.
Area orange is;
½*((sin54-cos54sin72)/sin72)((sin54sin72sin108+sin²54)/sin72sin108)
= 0.20143700267 square units.
Area green is;
½*((sin54)⁴/(sin108(sin72)²))
= 0.24898982848 square units.
Therefore;
Area Red ÷ (Area Green - Area Orange) is;
0.23776412908 ÷ (0.24898982848 - 0.20143700267)
= 0.23776412908 ÷ 0.04755282581
= 5.00000000063
= 5
