Mathematics Question and Solution
Calculating green area.
a² = 5²+5²
a = √(50)
a = 5√(2) units.
b = ½(a)
b = ½(5√(2)) units.
b = 3.53553390593 units.
5² = (5-c)²+(½(5√(2)))²
25 = 25-10c+c²+¼(50)
c²-10c+¼(50) = 0
4c²-40c+50 = 0
Notice;
c is the radius of the green circle.
c = 1.46447 units.
Therefore;
Green area is;
π(1.46447)²
= 6.73768699619 square units.
Calculating blue area.
d = 5-1.46447
d = 3.53553 units.
e = 45°
f = ½(e)
f = 22.5°
tan22.5 = g/5
g = 2.07106781187 units.
Area blue is;
2((½*2.07106781187*5)-(22.5π*25/360))
= 2(5.17766952968-4.90873852123)
= 0.5378620169 square units.
It implies;
Area Blue ÷ Area Green is;
0.5378620169÷6.73768699619
= 0.07982888151
≈ 0.08 to 2 decimal places.
