Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the square side be 1 unit.
Calculating Area Yellow.
Length CE is;
(CE/sin105)=(1/sin60)
CE = sin105/sin60
CE = (√(6)+√(2))/2√(3) units.
Area Yellow is;
Area triangle with height (√(6)+√(2))/2√(3)) units and base (√(6)+√(2))/2√(3))sin60
½*((√(6)+√(2))/2√(3))²sin60
= ¼((√(3)+2)/√(3)) square units.
Area Orange is;
Area triangle with height ½(√(6)-√(2)) units and base ⅙(3√(2)-√(6)) units.
= ½*½(√(6)-√(2))*⅙(3√(2)-√(6))
= ⅙(2√(3)-3) square units.
It implies;
Area Orange ÷ Area Yellow exactly is;
⅙(2√(3)-3) ÷ ¼((√(3)+2)/√(3))
= (4-2√(3))/(2+√(3)
= 2(7-4√(3))
