Mathematics Question and Solution
Let AB = 1 unit.
Therefore;
BC = 2AB = 2 units.
It implies;
AD = 4 units.
Calculating Area Red.
a² = 2²+1-2*2cos(180-(900/7))
a = 1.58304794386 units.
(1.58304794386/sin(180-(900/7))) = (2/sinb)
b = 180-81.02431846203
b = 98.97568153797°
c = 108-98.97568153797
c = 9.02431846203°
d = 180-(180-(900/7))-98.97568153797
d = 29.59574703346°
e = 180-51.42857142857-29.59574703346
e = 98.97568153797°
f = 180-98.97568153797-9.02431846203
f = 72°
(1.58304794386/sin72) = (g/sin98.97568153797)
g = 1.64413253907 units.
Area Red is;
0.5*2*1sin(51.42857142857)+0.5*1.64413253907*1.58304794386sin9.02431846203
= 0.78183148247+0.20412470079
= 0.98595618326 square units.
Calculating Area Blue.
h = 0.5(900/7)
h = 64.28571428571°
j = ½(108)
j = 54°
k = 180-64.28571428571-54
k = 61.71428571429°
l² = 32-32cos108
l = 6.472135955 units.
m² = 6.472135955²-2²
m = 6.15536707435 units.
n = (900/7)-90
n = 38.57142857143°
o = 2+4sin38.57142857143
o = 4.49395920744 units.
p² = 4.49395920744²-1
p = 4.38128626754 units.
q = 6.15536707435-4.38128626754
q = 1.77408080681 units.
(1.77408080681/sin61.71428571429) = (r/sin54)
r = 1.62987599889 units.
Area Blue is;
0.5*1.62987599889*1.77408080681sin64.28571428571
= 1.30259003334 square units.
Area Red ÷ Area Blue to 2 decimal places is;
0.98595618326÷1.30259003334
= 0.75691979673
= 0.76
