Calculating r/R.
Let let the ascribed square side length be 2 units.
Calculating R.
a = ½(2)
a = 1 unit.
b = (2-R) units.
Therefore;
(2-R)² = R²+1
4-4R+R² = R²+1
4-1 = 4R
R = ¾...
Calculating Shaded Fraction.
Let the ascribed square side length be 5 units.
a = 1 unit.
a is the side length of the big inscribed yellow square.
b = ½(5-a)
b = ½(5-1)
b = 2 units.
b is the side l...
Calculating the required angle.
Let it be x.
a = ⅑*180(9-2)
a = 20*7
a = 140°
a is the single interior angle of the regular nonagon.
b = ½(140)-65
b = 5°
c = ½(180(5-2)-3(140))
c = ½(540-420)
c...
Calculating Length x.
Let a be the side length of the blue square.
b² = 2a²
b = √(2)a units.
b is the diagonal of the blue square.
It implies;
x ~ 3
√(2)a ~ a
Cross Multiply.
a...
Calculating Red Area.
Let AB = CD = x.
Let AD = BC = y.
½*xa = 10
a = 20/x units.
a is BQ.
½*xb = 6
b = 12/x units.
b is the horizontal height of area 6 (area triangle APB).
c = y-b
c = y-(12/x...
Calculating area ABCD.
Let x be the radius of the inscribed circle.
a = ½(16)
a = 8 units.
x² = 8²+a²
a = √(x²-64) units.
b = ½(25) units.
It implies;
x ~ 8
½(25) ~ x
Cross Multiply.
x² = 10...
Calculating Area Yellow.
½*a²sin60 = 24
√(3)a² = 24*4
a² = 96/√(3)
a = √(96/√(3))
a = 7.44483887282 units.
a is the radius of the circle.
b = a-x
b = (7.44483887282-x) units.
Calcul...
Sir Mike Ambrose is the author of the question.
Let the single side length of the square be 2 units.
Area square is;
2² = 4 square units.
Calculating green area.
It will be;
Area square of side...
Let the single side length of the ascribed square be 2 units.
Calculating yellow area .
It is;
Area sector with radius 2 units and angle (90-2tan–¹(½))°).
= (90-2tan–¹(½))x4π÷360
= 1.287...
Calculating Area Red.
a = (1+x) units.
a is the diameter of the circle.
b = ½(a)
b = ½(1+x) units.
b is the radius of the circle.
c = ½(1-x) units.
Calculating x.
(½(1+x))² = 2(½(1-x))²
¼(1+2x+...
