Mathematics Question and Solution
a = 36+18
a = 54°
Let one of the green triangle area side be b.
cos54 = c/b
c = bcos54 units.
c = 0.5877852523b units.
sin54 = d/b
d = bsin54 units.
d = 0.8090169944b units.
e = c+d
e = 0.5877852523b+0.8090169944b
e = 1.3968022467b units.
Calculating b.
0.5*1.3968022467b*bsin54 = 22
1.3968022467b² = 44
b² = 31.500522071
b = 5.6125325897 units.
e = 1.3968022467b units.
And b = 5.6125325897 units.
e = 1.3968022467*5.6125325897
e = 7.839598131 units.
f² = 7.839598131²+5.6125325897²-2*7.839598131*5.6125325897cos54
f = 6.4214265334 units.
f is the side length of the bigger regular pentagon.
sin54 = (0.5*5.6125325897)/g
g = 3.4687359034 units.
g is the side length of the big regular pentagon.
(7.839598131/sinh) = (6.4214265334/sin54)
h = 81°
j = 360-81-108-72
j = 99°
k² = 6.4214265334²+3.4687359034²-2*6.4214265334*3.4687359034cos99
k = 7.7611701995 units.
k is the side length of the biggest regular pentagon.
(7.7611701995/sin99) = (3.4687359034/sinl)
l = 26.1952933695°
m = 360-(2*108)-26.1952933695
m = 117.8047066305°
n² = 2(7.7611701995²)-2(7.7611701995²)cos108
n = 12.5578371753 units.
It implies, area red is;
Area triangle with height 12.5578371753 units and base 6.4214265334sin117.8047066305
= 0.5*12.5578371753*6.4214265334sin117.8047066305
= 35.6644190027 square units.
