Mathematics Question and Solution
Let the side length of the regular nonagon be 1 unit.
a = ⅑(180(9-2))
a = ⅑(180*7)
a = 140°
Area Nonagon is;
0.5*9*0.5tan(70)
= ¼(9tan70)
= 6.18182419377 square units.
b = 540-3*140
b = 120°
c = ½(b)
c = 60°
d = 140-60
d = 80°
(e/sin30) = (1/sin50)
e = 0.65270364467 units.
sin80 = f/1
f = 0.98480775301 units.
(1/sin20) = (g/sin80)
g = 2.87938524157 units.
sin80 = h/2.87938524157
h = 2.83564090981 units.
j = 180-40-80
j = 60°
(1/sin60) = (k/sin40)
k = 0.74222719897 units.
(0.74222719897/sin100) = (l/sin20)
l = 0.25777280103 units.
It implies;
Area Purple is;
(0.5*2.83564090981*1) - (0.5*0.25777280103*0.74222719897sin60) - 0.5(1+0.65270364467)0.98480775301
= 1.4178204549-0.08284658131-0.81379768135
= 0.52117619224 square units.
Therefore;
Area Nonagon ÷ Area Lilac to 2 decimal places is;
6.18182419377÷0.52117619224
= 11.86129429129
≈ 11.86
