Mathematics Question and Solution
Let the bigger white semi circle's radius be a.
b = ½(a) units.
b is the radius of the smaller white circle.
c = a+b
c = a+½(a)
c = ½(3a) units.
c is the radius of the bigger white and green semi circle.
Therefore;
Calculating a.
(½(3a))² = 2²+(a/2)²
(9a²/4) = 4+(a²/4)
2a² = 4
a² = 2
a = √(2) units.
Again, a is the radius of the bigger white semi circle.
b = ½(a)
And a = √(2) units.
b = ½√(2) units.
b = 0.5√(2) units.
Again, b is the radius of the smaller white semi circle.
c = ½(3a)
And a = √(2) units.
c = ½(3√(2)) units.
c = 0.5(3√(2)) units.
Again, c is the radius of the bigger green and white semi circle.
d = 2c-a
d = 2*0.5(3√(2))-√(2)
d = 3√(2)-√(2)
d = 2√(2) units.
d is the diameter of the smaller white and green semi circle.
e = ½(d)
e = ½*2√(2)
e = √(2) units
e is the radius of the smaller white and green semi circle.
Area green is;
Area semi circle with radius 0.5(3√(2)) units + Area semi circle with radius √(2) units - Area semi circle with radius √(2) units - Area semi circle with radius 0.5√(2) units.
= 0.5π(0.5(3√(2)))²+0.5π(√(2)²)-0.5π(√(2)²)-0.5π(0.5√(2))²
= ¼(9π)+π-π-¼(π)
= ¼(8π)
= 2π square units.
