Mathematics Question and Solution
Calculating R, radius of the four inscribed equal half circles.
Notice!
Radius of the four equal inscribed circles is 1 unit.
Therefore;
(2R-1)² = 1²+a²
4R²-4R+1 = 1+a²
a = √(4R²-4R) units.
It implies;
(R+1)² = a²+(R-1)²
(R+1)² = √(4R²-4R)²+(R-1)²
R²+2R+1 = 4R²-4R+R²-2R+1
8R = 4R²
4R = 8
R = 2 units.
2R = 2*2 = 4 units.
Where 2R = 4 units is the radius of the ascribed circle.
Therefore, area yellow is;
Area circle with radius 4 units - 2(area circle with radius 2 units) - 4(area circle with radius 1 unit).
= π(4²)-2π(2²)-4π(1²)
= 16π-8π-4π
= 16π-12π
= 4π square units.
