Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Orange ÷ Area Quadrilateral ABCD Exactly.
Area Orange (trapezoid) is;
Area trapezoid with parallel sides ⅔ units and ½ units, and height √(3)/6 units.
= ½*(√(3)/6)(½+⅔)
= 7√(3)/72 square units.
Area quadrilateral ABCD is;
Area trapezoid with parallel sides ⅔ units and ½ units, and height √(3)/6 units + 2(area triangle with height ⅓√(3) units and base ⅓ units + Area triangle with height (√(3)/6) units and base ½ units + Area triangle with height ½ units and base ½√(3) units.
= (7√(3)/72) + (2*½*⅓*⅓√(3)) + (½*½*(√(3)/6)) + (½*½*½√(3))
= 7√(3)/72 + √(3)/9 + √(3)/24 + √(3)/8
= (7√(3)+8√(3)+3√(3)+9√(3))/72
= 27√(3)/72 square units.
Therefore;
Area Orange ÷ Area Quadrilateral ABCD Exactly is;
(7√(3)/72) ÷ (27√(3)/72)
= 7/27
