Top 10.731

X = 2

Square Area = 48

Orange = 37.8797121309

R2 = 1.61803398875

X = AE = 5

Blue Area = 11.7393568819

X = PQ = 15

Easy Way

Triangle Area = 1

X = Height = 4.8 = 24 / 5

X = 14.1421356237 = 10 √ 2

Top 10.730

Shaded = 12.7470644749

X = ADG = AGP = 15

Orange Area = 3.5 = 7 / 2

X = ABD = 30

Blue Area = 19.5075774975

1 / 7 = 0.142857142857

Max ( R ) = 0.429357840223

Shaded Area = 6

Without Trigonometry

Regular Heptagon. DH = √ 2

Blue Area = 6 Square Units

Top 10.729

Radius R =5.83363094479

Orange / Green = 2.25 = 9 / 4

β = ( 360 - 𝛼 ) / 2

Blue Square Area = 25

Ratio of BD : BE = 1 : 2

X = AFC = 49.1066053509

Blue Triangle Area = 4

Pink Area = 21.9911485751

X = DL = 8.48528137424

Solution = 0.464101615138

Top 10.728

Circle Area = 62.8318530718

X = ACB = 30

Triangle AKD Area = 88.5894030641

Area of Yellow Squares = 60

EAD = DAF = 45

Pink Fraction = 9 / 14

X = 1.8612097182

Orange = 113.490034611

X = BD = 3.46410161514

Simplified / Improved

Blue Area = 36

Top 10.727

X = ACB = 6

ADM = BAD = 15

Mathematical Proof

Red Fraction of Rectangle

Elaborated / Improved

Radius R = 3.88131944636

X = AE = 4

Green Fraction = 1 / 3

Red / Blue = 0.259921049895

Blue Area / Red Area = 1

Blue Area = 19.3923048454