Let the single side length of the regular pentagon be 1 unit.
Therefore;
Area blue is;
½(sin108) square unit.
Area red is;
(1-cos36)sin108 square unit.
Therefore;
Area blue : Area red is;
½(sin108) ÷ (1-cos36)sin108
= 1 ÷ (2-2cos36)
= 2.61803398875
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