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Calculating Blue Area.
a = 8+2
a = 10 units.
a is the side length of the ascribed square and the radius of the bigger inscribed quarter circle.
b = 8 units.
b is the radius of the big insc...
Let angle AOB be a.
Let b = AD = OB = OD.
b is the radius of the quarter circle.
Calculating b.
2² = 2b²-2b²cosa
2b²cosa = 2b²-4
b²cosa = b²-2
cosa = (b²-2)/b² --- (1).
4² = b²+(2b)²-4b²cosa
16...
Let r = 1 unit.
a = (R+1) units.
b = (R-1) units.
c²+b² = a²
c²+(R-1)² = (R+1)²
c² = R²+2R+1-(R²-2R+1)
c = √(4R)
c = 2√(R) units.
d = R+2-R
d = 2 units.
e = R+R
e = 2R units.
Calculating R....
Notice.
The ascribed quadrilateral is regular (square).
Let a be it's side length.
½*ab = 3
ab = 6
b = (6/a) units.
b is the base of the red area.
½*ac = 4
ac = 8
c = (8/a) units....
