Mathematics Question and Solution
Calculating Area Blue.
a = ½(4)
a = 2 units.
a is the radius of the inscribed half circle.
b = (2+x) units.
x is the radius of the inscribed circle.
c = (4-x) units.
It implies;
d²+x² = (4-x)²
d² = 16-8x+x²-x²
d = √(16-8x) units.
e = (2-x) units.
Calculating x.
(2+x)² = (2-x)²+√(16-8x)²
4+4x+x² = 4-4x+x²+16-8x
16x = 16
x = 1 units.
Again, x is the radius of the inscribed circle.
Therefore, Blue Area is;
Area quarter circle with radius 4 units-Area half circle with radius 2 units-Area circle with radius 1 unit.
= ¼(π*4²)-½(π*2²)+(π*1²)
= 4π-2π-π
= π square units.
