Le the side of the pentagram be 1 unit.
tan54 = a/0.5
a = 0.68819096024 unit.
cos54 = 0.5/b
b = 0.85065080835 unit.
c = b+a
c = 1.53884176859 units.
Let the side length of the ascrib...
Let the inscribed purple regular heptagon side be 1 unit.
a = ⅐(180*5)
a = ⅐(900)°
b = 180-⅐(900))
b = ⅐(360)°
c = 180-2(⅐(360))
c = ⅐(540)°
(1/sin⅐(540)) = (d/sin⅐(360))
d = 0.8019...
Let the side of the regular pentagon be 1 unit.
a² = 2-2cos108
a = 1.61803398875 units.
sin30 = b/0.5
b = 0.25 unit.
c = 2b
c = 0.5 unit.
Where c is the inscribed square side.
Are...
a = asin(1/3)°
a = 19.47122063449°
a = angle ABF.
Let the centre of the diameter of the half circle be O.
Angle AOF = 90-19.47122063449 = 70.52877936551°
(OC)² = 12²+18²
OC = 6√(13) c...
Let the side of the regular pentagon be 1 unit.
Notice;
The regular pentagon side is equal the regular heptagon side.
a = ⅐(180*5)
a = ⅐(900)°, the single interior angle of the regular he...
a = 360-140-80
a = 140°
cos20 = 1/b
b = 1.06417777248 units.
(1.06417777248/sin30) = (c/sin70)
c = 2 units.
d² = 4+1.064177772482²-4*1.06417777248cos140
d = 2.89711998506 units.
(2...
Let the side of the regular pentagon be 1 unit.
a = 360-2(108)-90
a = 54°
tan72 = b/0.5
b = 1.53884176859 units.
tan54 = 1.53884176859/c
c = 1.11803398875 units.
d = c-0.5
d = 0.618...
Notice;
The diameter of the semicircle is 8 units.
Therefore radius is 4 units.
tan30 = a/2
a = ⅔(√(3)) units.
b = 3a
b = 2√(3) units.
c² = 2²+(⅔(√(3)))²
c = (4/√(3)) units.
d...
Let the side of the regular hexagon which is equal the side of the square be 1 unit.
a = ½(180-108)
a = 36°
tan36 = b/0.5
b = 0.363271264 unit.
Area Blue is;
0.5*0.363271264*0.5
=...
Sir Mike Ambrose is the author of the question.
Let the side of the inscribed square be 2 units.
Therefore;
Area S is;
Area triangle with two side 1.03528 units and 0.53589838486 units, and angl...
