Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Yellow Area.
It is;
Area triangle with height 4sin(atan(⅔)) units and base 8√(13)/9 units - Area triangle with height 1 unit and base ⅔ unit - Area triangle with height ¼ unit and base ⅔ unit
= ½*4sin(atan(⅔))*(8√(13)/9) - ½*1*⅔ - ½*¼*⅔
= (32/9)-⅓-(1/12)
= (113/36) square units.
Area Orange is;
Area triangle with height ⅓(10sin(atan(¾))) units and base (5√(13)/9) units.
= ½*⅓(10sin(atan(3/2)))*(5√(13)/9)
= (25/9) square units.
Area Blue is;
Area trapezium with parallel sides 2 unit and units 3.5 units, and height 2 units - Area triangle with height 4sin(atan(⅔)) units and base 8√(13)/9 units + Area triangle with height (5/12) unit and base ½(sin(atan(4/3))) unit.
= ½*2(2+3.5) - (32/9) + ½*(5/12)*½(sin(atan(4/3)))
= (11/2) - (32/9) + (1/12)
= (73/36) square units.
Therefore;
Area Blue : Area Orange : Area Yellow is;
(73/36) : (25/9) : (113/36)
= 73 : 100 : 113
