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 units.
Area Blue is;
0.5*0.363271264*0.5
= 0...
Let the regular pentagon side be 1 unit.
sin72 = a/1
a = 0.9510565163 units.
Let the side of the two inscribed congruent squares be b.
c = ½(b) units.
b+½(b) = 0.9510565163
b = 0.6340...
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...
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...
Let AB be 5 units.
Radius, r of the inscribed circle is;
r = 5*(2/5)
r = 2 units.
a = ⅛(180*6)
a = 135°
2b² = 25
b = ½(5√(2)) units.
c = 180-0.5(135)-45
c = 67.5°
sin22.5 = ½...
Sir Mike Ambrose is the author of the question.
Let the side length of the square be 2 units.
Therefore area ABD (equilateral triangle) is;
Area triangle with height 2 unit and base (2sin6...
18² = 14²+16²-2*14*16cosa
448cosa = 14²+16²-18²
a = acos((14²+16²-18²)/448)
a = 73.39845040098°
(18/sin73.39845040098) = (14/sinb)
b = 48.18968510422°
c = 180-48.18968510422-73.3984504009...
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 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...
Sir Mike Ambrose is the author of the question.
Let the single side length of the square be 2 units.
Therefore;
Area Square is;
2²
= 4 square units.
Area Green is;
Area triangl...
