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...
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a = atan(½)°
b² = 2(10)²
b = 10√(2) units.
c = (45-atan(½))°
cos(atan(½)) = d/20
d = 17.88854382 units.
Area x is;
0.5*17.88854382*10√(2)sin(45-atan(0.5))
= 40 square units.
Let the side length of the regular heptagon be 1 unit.
a = ⅐(180*5)
a = ⅐(900)°
b = 0.5(360-2(900/7))
b = ⅐(360)°
c = 2cos(360/7)+1
c = 2.24697960372 units.
d² = 2-2cos(90/7)
d = 1.8019377358 un...
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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 = 180-48.18968510422-73.39845040098
c = 58....
Let AB be 5 units.
Radius, r of the inscribed circle is;
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(5√(2))/d
d = 9.23879...
