Mathematics Question and Solution
Let AB be 2 unit.
Therefore CD = 1 unit.
It implies;
Area Blue is;
Area triangle with height 0.72111025509 unit and base sin(atan(3/2)) unit.
= 0.5*0.72111025509sin(atan(3/2))
= 3/10 space unit.
Area Green is;
Area trapezoid with two parallel side (3/2) unit and 1 unit, and height ½ unit - Area triangle with height (3/2) unit and base ½ unit.
= ½*½((3/2)+1) - ½*½(3/2)
= (5/8) - (3/8)
= ¼ space unit.
Area Red is;
Area triangle with height tan(atan(2/3)) unit and base √(2)sin45 unit - Area triangle with height tan(atan(2/3)) unit and base (½√(2)sin45) unit.
= ½(√(2)sin45)(tan(atan(2/3))) - ½((½√(2)sin45)(tan(atan(2/3)))
= ⅓ - (1/6)
= 1/6 space unit.
Therefore;
Area Red : Area Green : Area Blue is;
(1/6) : (¼) : (3/10)
= 60(1/6) : 60(¼) : 60(3/10)
= 10 : 15 : 18
