Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the side of the regular hexagon be 2 units.
Therefore;
Area Green is;
Area regular equilateral triangle with side √(3) units.
½*√(3)*√(3)sin60
= ¼(3√(3)) square units.
Area Blue is;
Area trapezoid with parallel sides √(3) units and 2√(3) units, and height ½ unit - Area triangle with height ⅓√(3) units.
½*½(√(3)+2√(3)) - ½*1*⅓√(3)
= ¼(3√(3))-√(3)/6
= 7√(3)/12 square units.
Area Orange is;
Area trapezoid with parallel sides 1 unit and ½ unit, and height ½√(3) units.
½*½√(3)(1+½)
= ⅛(3√(3)) square units.
It implies;
Area Orange : Area Blue : Area Green in a : b : c form, where a, b and c are integers is;
⅛(3√(3)) : 7√(3)/12 : ¼(3√(3))
= ⅛(3) : (7/12) : ¼(3)
= 9 : 14 : 18
