Top 10.688

Blue Area = 6.82427610338

Simplified / Improved

B, E, M are Collinear Points

Blue Area = 14.7614538495

Yellow Area = 12 √ 3

Proof that BCL is Equilateral

Shaded = 25.1327412287

Radius R = 4.74341649025

X = ABC / 2 = 15

Blue Area = 3.75 = 15 / 4

ELF = 22.5 = 45 / 2

Top 10.687

R = 1.61803398875

Radius R = 5

Blue Area = 25.0404465894

Diameter = 9

Easy Way by Means of Regression

Proof that b = 2 d

Circular Segment CD = 6

Blue Area = 20.7846096908

Green Triangle Area = 12

Segment X = 1.3416407865

Segment DF = 4

Top 10.686

Shaded = 18 Square Units

Find the Blue Area ( Animation )

Total = 450 Square Units

sin AEF = 0.292828901981

Radius R = 21.25 = 85 / 4

Ratio of AC / DE = 3

Radius R = 3.5

Another Approach

Blue Area = 6 + ( 12 / X )

Orange = 64.2743338823

Solution = 1.61803398875

Top 10.685

Orange Area = 121.630162362

Animation. Missing R₃ = 3

Coordinates of A, B, C and D

GJ / IJ = 1.61803398875

Radius R = 3

X = LM = 10.5409255339

Red Area = 1 / 2 Square Units

Yellow Area = 88.5896103705

Pink Area = 1.08471306274

h = 1 for min Box Surface Area

Top 10.684

Radius R = 1.78361162489

Improved / Elaborated

LM = 0.76536686473

X = KL = 5

Simplified / Improved

Blue Area = 21.1660104885

Ratio of Pink / Green = 4

Proof that CAF = 45°

Semicircle = 282.743338823

3 Blue Area = Total Area

Total Area = 254.611468713

X = 19.0702347117