Mathematics Question and Solution
a = ½(d) units.
a is the radius of the green half circle.
b = d+a
b = ½(3d) units.
c² = (½(3d))²-(½(d))²
c² = ¼(8d²)
c = √(2(d)²)
c = √(2)d units.
c is the diameter of the small blue semi circle.
d = ½(c)
d = ½√(2)d units.
d = 0.7071067812d units.
d is the radius of the small blue semi circle.
tane = ½(d)/√(2)d
e = atan((½)/√(2))
e = atan(¼√(2))
f² = (3d)²+(√(2)d)²-2*3d*√(2)dcos(0.25√(2))
f = 1.5858373728d units.
f is the diameter of the big semi circle.
g = ½(f)
g = 0.7929186864d units.
g is the radius of the big semi circle.
Therefore, area blue total with respect to d is;
0.5π(0.7071067812d)²+0.5π(0.7929186864d)²
= 0.9875911345d²+0.7853981634d²
= 1.7729892979d² square units.
