Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the single side length of the congruent regular hexagons be 1 unit.
Therefore;
Area red is;
Area trapezium with two parallel side length ½(3√(3)) unit and 2√(3) unit, and height ½ unit + Area triangle with height 2√(3) unit and base 2 unit.
½*½(½(3√(3))+2√(3)) + ½(2√(3)*2)
= (7√(3))/8 + 2√(3)
= (23√(3)/8) square unit.
Area orange is;
Area trapezium with two parallel side length 1 unit and 2 unit, and height ½√(3) unit + Area trapezium with two parallel side length 3 unit and ½(5) unit, and height ½√(3) unit
= ½*½√(3)(1+2) + ½*½√(3)(3+½(5))
= ¼(3√(3)) + (11√(3))/8
= (17√(3))/8 square unit.
It implies;
Area Orange ÷ Area Red exactly in its simplest form is;
(17√(3))/8 ÷ (23√(3)/8)
= 17/23
