Mathematics Question and Solution
Calculating Blue Area.
a = 8+2
a = 10 units.
a is the side length of the ascribed square and the radius of the bigger inscribed quarter circle.
b = 8 units.
b is the radius of the big inscribed quarter circle.
c = ½(a)
c = 5 units.
c is the radius of the inscribed half circle.
8² = 2*5²-2*5²cosd
50cosd = 50-64
d = acos(-7/25)
d = 106.260204708°
d' = ½(180-d)
d' = 36.869897646°
e = 180-d
e = 73.7397952917°
f = 180-2e
f = 32.5204094166°
g² = 2*5²-2*5²cos32.5204094166
g = 2.8 units.
h = ½(10-g)
h = 3.6 units.
cosj = 3.6/8
j = 63.2563160496°
j' = 90-j
j' = 26.7436839504°
k = 180-2j
k = 53.4873679008°
It implies;
Area Blue is;
Area quarter circle with radius 8 units - Area sector with radius 8 units and angle 36.869897646° - Area sector with radius 5 units and angle 106.260204708° + Area triangle with height 5 units and base 5sin106.260204708 units - Area sector with radius 8 units and angle 26.7436839504° + Area sector with radius 10 units and angle 53.4873679008° - Area triangle with height 10 units and base 10sin53.4873679008 units.
= (¼*8²π)-(36.869897646π*8²/360)-(106.260204708π*5²/360)+(½*5²sin106.260204708)-(26.7436839504π*8²/360)+(53.4873679008π*10²/360)-(½*10²sin53.4873679008)
= 50.2654824574-20.5920354815-23.18238045+12-14.9364908495+46.6765339047-40.1862849739
= 10.0448246072 square units.
