Calculating Area Blue.
Let a be the side length of the ascribed quarter circle.
tan30 = 2/b
b = 2√(3) units.
c = (a-2) units.
d = (2√(3)+½(a))
d = ½(4√(3)+a) units.
Calculating a.
(a-2)² = (½(...
Calculating Area Yellow, Area of The Inscribed Half Circle.
4r+3r = 4*3
7r = 12
r = ⅐(12) units.
r is the radius of the inscribed yellow half circle.
Area Yellow Inscribed Half Circle is;...
Calculating Area Green.
sin30 = a/12
a = 6 units.
b²+6² = 12².
b = √(144-36)
b √(108)
b = 6√(3) units.
sin60 = c/12
c = 6√(3) units.
d² = 12²-(6√(3))²
d = √(144-108)
d = √(36)
d = 6 units.
The...
Calculating Shaded Green Area.
sin30 = a/2
a = 1 unit.
(a')²+1² = 2²
a' = √(4-1)
a' = √(3) units.
a'' = 2a'
a'' = 2√(3) units.
a'' is the side length of the inscribed regular triangle.
b² = 2²+2...
Calculating Length x.
x ~ ½(2)
(2+7) ~ x
Cross Multiply.
x² = 9
x = √(9)
x = 3 units.
Calculating Area Blue Triangle.
a² = 2(2)²
a = 2√(2) units.
a is the diagonal of a square.
b = ½(180-30)
b = 75°
c = b-45
c = 75-45
c = 30°
sin30 = d/a
½ = d/(2√(2))
d = √(2) units.
d is the bas...
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...
