Mathematics Question and Solution
Let a be the congruent side lengths each.
b = ½(2)
b = 1 unit.
c²+1² = a²
c = √(a²-1) units.
d = ½(180-45)
d = ½(135)
d = 67.5°
tan67.5 = e/1
e = 2.4142135624 units.
e = (1+√(2)) units.
f = 1+e
f = (2+√(2)) units.
f is the radius of the ascribed quarter circle.
g = f-2
g = √(2) units.
Therefore, blue area is;
½*(fg)
= ½*(2+√(2))*√(2)
= ½(2+2√(2))
= (1+√(2)) square units.
= 2.4142135624 square units.
