Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the square aide length be 1 unit.
Square Area is;
1²
= 1 square unit.
Calculating Green Area.
a² = 1²+1²
a = √(2) units.
a is AB.
b = ½(a)
b = ½√(2) units.
sin60 = c/√(2)
2c = √(6)
c = ½√(6) units.
Or
tan60 = c/(½√(2))
√(3) = 2c/√(2)
c = ½√(6) units.
tan60 = √(2)/d
d = ⅓√(6) units.
It implies, area green is;
Area right-angled trapezium with parallel lengths √(2) units and ½√(2) units respectively and height ½√(6) units - Area triangle with height √(2) units and base ⅓√(6) units - Area triangle with height √(2) units and base √(2)sin30 units.
= ½((½√(2)+√(2))*½√(6))-½(⅓√(6)*√(2))-½(√(2)²*sin30)
= ¼(3√(3))-⅓√(3)-½
= (9√(3)-4√(3)-6)/12
= (5√(3)-6)/12 square units.
Therefore;
Green Area ÷ Square Area exactly is;
(5√(3)-6)/12 ÷ 1
= (5√(3)-6)/12
= 0.22168783649 in decimal.
