Mathematics Question and Solution
Let CE be 3 units.
Therefore:
Area Orange is;
Area triangle with height √(19) units and base 6sin(60-acos(4/√(19))) units - Area triangle with height (12√(19)/19) units and base (36√(57)/133) units.
= ½*√(19)*6sin(60-acos(4/√(19))) - ½*(12√(19)/19)*(36√(57)/133)
= ½(9√(3)) - (216√(3))/133
= (765√(3)/266) square units.
Area ACEB is;
Area trapezium with parallel sides 3 units and 6 units, and height ½(3√(3)) units.
= ½*½(3√(3))*(3+6)
= ¼*9*3√(3)
= ¼(27√(3)) square units.
It implies;
Area Orange ÷ Area ACEB exactly is;
(765√(3)/266) ÷ ¼(27√(3))
= 170/399
