Mathematics Question and Solution
Let the regular triangle side length be 2 units.
Therefore the square side length is 1 unit.
a² = 2(1²)
a = √(2) units.
b² = 2+1-2√(2)cos105
b = √(3-2√(2)cos105) units.
(√(3-2√(2)cos105)/sin105) = (√(2)/sinc)
c = 45°
(1/sin75) = (d/sin45)
d = 0.7320508076 units.
d = (√(3)-1) units.
Area Blue is;
0.5*1*0.7320508076sin60
= 0.3169872981 square units.
= ¼(3-√(3)) square units.
Calculating Area Red.
sin30 = e/1
e = ½ units.
(2/sin75) = (f/sin45)
f = 1.4641016151 units.
f = (2√(3)-2) units.
g = (2√(3)-2)-½
g = ½(4√(3)-4-1)
g = ½(4√(3)-5) units.
g = 0.9641016151 units.
sin60 = h/1
h = √(3)/2 units.
j² = (√(3)/2)²+(sin(45)/sin(75))²
j = 1.1339745962 units.
k = 90-atan((√(3)-1)/(sin60))
k = 49.792181278°
Area Red is;
0.5*1.1339745962*0.9641016151sin49.792181278 + Area Blue.
=
0.4174682452+0.3169872981
= 0.7344555433 square units.
It implies;
Area Red ÷ Area Blue exactly in decimal is;
0.7344555433÷0.3169872981
= 2.3169872981
≈ 2.32 to 2 decimal places.
