Mathematics Question and Solution
Let the ascribed quarter circle radius be 1 unit.
2a² = 1²
a² = ½
a = ½√(2) units.
a = 0.7071067812 units.
a is the radius of the blue inscribed quarter circle.
Area blue inscribed quarter circle (S2) is;
¼*πa²
= ¼(½√(2))²π
= ⅛π square units.
c = (1-b) units.
b is the radius of the yellow inscribed semi circle.
It implies, calculate b.
(1-b)² = b²+(½√(2))²
1-2b+b² = b²+½
2b = ½
b = ¼ units.
b = 0.25 units.
Again, b is the radius of the yellow semi circle.
Area yellow semi circle (S1) is:
½*πb²
= ½*(¼)²π
= π/32 square units.
It implies;
S1 ÷ S²
= (π/32)÷(π/8)
= ¼
