Mathematics Question and Solution
Let s be 4 units.
It implies;
r = ¼(5*4)
r = 5 units.
a² = 32-32cos108
a = 6.472135955 units.
b = ½(a)
b = 3.2360679775 units.
Notice;
Angle BGC = 36°
cos18 = c/4
c = 3.80422606518 units.
sin18 = d/4
d = 1.2360679775 units.
tan36 = 3.80422606518/e
e = 5.2360679775 units.
Calculating BG.
BG = d+e
BG = 1.2360679775+5.2360679775
BG = 6.472135955 units.
Area Green plus Area Blue is;
0.5*6.472135955*6.472135955sin36
= 12.3107341487 square units.
Let x and y be BF and FG respectively.
Therefore;
x+y = 6.472135955
tan36 = 5/f
f = 6.88190960236 units.
f is AF.
Therefore;
x (BF) = 6.88190960236-4
x = 2.88190960236 units.
And;
x+y = 6.472135955
y = 6.472135955-2.88190960236
y (FG) = 3.59022635264 units.
It implies;
Area Green is;
0.5*2.88190960236*3.80422606518
= 5.4817178134 square units.
Area Blue is;
(Area Green plus Area Blue)-(Area Green)
= 12.3107341487-5.4817178134
= 6.8290163353 square units.
Therefore;
Area Green/Area Blue is;
5.4817178134/6.8290163353
= 0.80270972337
≈ 0.80 to 2 decimal places.
