Top 10.712

Purple Area = 64 / 3

Green / Rectangle = 0.24 = 6 / 25

Green / Blue = 1.61803398875

There are Many Solutions

Orange Area = 27.0338614318

Improved / Elaborated

Mathematical Proof

Missing Angle CAO = 55

Green / Total = 5 / 24

Green Area = 14.7

Segment BC = 4