Mathematics Question and Solution
Let the radius of the semi circle be 1 unit.
cos60 = a/1
a = ½ units.
sin60 = b/1
b = √(3)/2 units.
Where b is the side length of the square.
Area Square is;
(√(3)/2)²
= ¾ square units.
= 0.75 square units.
c² = 1²+(3/4)-2*(√(3)/2)cos120
c = √(¼(2√(3)+7)) units.
c = 1.6174131828 units.
(1.6174131828/sin120) = (1/sind)
d = 32.373659127°
e = 45-d
e = 45-32.373659127
e = 12.626340873°
(1/sin12.626340873) = (1.6174131828/sinf)
f = 20.7048110551°
g = 180-135-f
g = 45-20.7048110551
g = 24.2951889449°
h = 90-24.2951889449
h = 65.7048110551°
j = 180-65.7048110551
j = 114.2951889449°
tan24.2951889449 = k/0.5
k = 0.2257081148 units.
cos24.2951889449 = 0.5/l
l = 0.5485837704 units.
m = 1-0.5485837704
m = 0.4514162296 units.
It implies;
Area Blue is;
0.5*0.4514162296*0.2257081148sin114.2951889449
= 0.0464324282 square units.
Therefore;
Area Blue ÷ Area Square exactly in decimal is;
0.0464324282 ÷ 0.75
= 0.0619099043
≈ 0.062 to 3 decimal places.
