Mathematics Question and Solution
Notice!
R is the radius of the ascribed semi circle.
Calculating R.
a² = 2*√(2)²
a² = 4
a = 2 units.
a is the diagonal of the inscribed red and white square.
√(2)² = 2b²
b² = 2/2
b = 1 unit.
It implies;
R² = 2²+1²
R² = 5
R = √(5) units.
Again, R is the radius of the ascribed semi circle.
tanc = 2/(√(5)+1)
c = atan(2/(√(5)+1))°
c = 31.7174744115°
tan(atan(2/(√(5)+1))) = d/√(5)
d = 1.3819660112 units.
e = d-b
e = 1.3819660112-1
e = 0.3819660112 units.
Therefore, white area is;
Area triangle with height and base √(2) units respectively + Area triangle with height and base 1 unit respectively + Area triangle with height √(2) units and base 0.3819660112sin45 units.
= ½*√(2)²+½*1²+½*√(2)*0.3819660112sin45
= 1+½+0.1909830056
= 1.6909830056 square units.
