Mathematics Question and Solution
(6/sin(180-45-atan(2))) = (a/sin45)
a = 4.472135955 cm.
b = √(12²+6²)+a
b = 17.88854382 cm.
c² = 4.472135955²+6²-12*4.472135955cos(180-atan2)
c = 8.94427191 cm.
Where c is CF.
(8.94427191/sin(180-atan2)) = (6/Sind)
d = 36.86989764584°
d is angle CFD.
Angle BCF is;
180-(180-atan2)-36.86989764584°
= atan2-36.86989764584°
= 26.56505117708°
Angle ECF is;
90-26.56505117708
= 63.43494882292°
Notice;
atan(½)+63.43494882292 = 90°
It implies;
sin(atan(½)) = e/12
e = 5.366563146 cm.
cos(atan(½)) = f/12
f = 10.733126292 cm.
g = CF-5.366563146
g = 8.94427191-5.366563146
g = 3.577708764 cm.
Therefore, Area Shaded Region is;
0.5*3.577708764*10.733126292
= 19.2 cm²
= 19⅕ cm²
