Mathematics Question and Solution
Calculating Area Red/Area Yellow.
Let R, radius of the equal circles be 1 unit.
Area Yellow is;
2(2(area sector with radius 1 unit and angle 60°) - area regular triangle with side length 1 unit)
= 2(2(60π/360)-½*sin60)
= 2(⅓(π)-¼(√(3)))
= ⅔(π)-½√(3)
= ⅙(4π-3√(3)) square units.
= 1.2283696986 square units.
Area Red is;
Area circle with radius 1 unit - Area yellow.
= π-⅙(4π-3√(3))
= ⅙(6π-4π+3√(3))
= ⅙(2π+3√(3)) square units.
= 1.913222955 square units.
Therefore, Area Red/Area Yellow is;
⅙(2π+3√(3))÷⅙(4π-3√(3))
= (2π+3√(3))÷(4π-3√(3)) exactly in fraction.
= 1.5575302429 exactly in decimal.
