Let the side length of the regular pentagon be 1 unit.
tan36 = a/0.5
a = 0.363271264 unit.
b² = 0.363271264²+0.5²
b = 0.61803398875 unit.
tan72 = c/0.5
c = 1.53884176859 units.
Area Green is;
0...
a = asin(1/6)
b = 2a
b = 2asin(1/6)
Where b is angle BAC
cos(2asin(1/6)) = c/6
c = ⅓(17) units.
Where c is AD.
d = 6-c
d = 6-⅓(17)
d = ⅓ units
Where d is CD.
sin(2asin(1/6)) = e/6
e = 1.97202659...
Let the radius of the ascribed circle be 2 units.
sin10 = a/2
a = 0.34729635533 units.
a is O1D.
cos10 = b/2
b = 1.96961550602 units.
b is CD.
Let the small inscribed circle radius be r.
Calcula...
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Let the small square side length be 1 unit.
(a/sin30) = (1/sin15)
a = 1.93185165258 units.
a is the big square side length.
b² = 1.93185165258²+1-2*1.93185165258cos45
b = √(2) units.
b = 1.4142135...
Radius of the circle r, is;
πr² = 25π
r = 5 cm.
Therefore diameter is;
2r
= 10 cm.
Let the side of the small yellow Inscribed square be x.
a² = 2x²
a = √(2)x cm.
Where a is a diagonal of the sma...
r = √(3²+4²)
r = 5 units.
r is the radius of the quarter circle.
(5-x)² = x²+(3+x)²
x is the radius of the inscribed yellow circle.
Therefore;
25-10x+x² = x²+9+6x+x²
x²+16x-16 = 0
(x+8)² = 16+64
x...
Let the square side be 3 cm.
Therefore;
Observing similar triangle ratios.
3 = 2
1 = a
Cross Multiply.
a = ⅔ units.
b = √(3²+1²)
b = √(10) cm.
c = √(2²+(⅔)²)
c = ⅓(2√(10)) cm.
d = √(√(10)²+(⅓(2√(...
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Let the side of the regular hexagon be a.
Calculating a
b = 180-60-45
b = 75°
(c/sin75) = (2/sin45)
c = (1+√(3)) units.
d² = 2a²-2a²cos120
d = √(3a²)
d = √(3)a ----- (1).
e = c+a, and c = (1+√...
