Mathematics Question and Solution
Let the square side length be 1 unit.
Therefore, the regular hexagon side length a, is;
a = 5*1
a = 5 units.
b² = 2(5)²-2(5)²cos120
b = 5√(3) units.
Area regular hexagon is;
2(½*5*5sin120)+(5√(3)*5)
= ½(25√(3))+25√(3)
= ½(75√(3)) square units.
Calculating the inscribed blue area.
tan30 = c/1
c = ⅓√(3) units.
Blue Area is;
6(area rectangle with length 1 unit and width ⅓√(3) units).
= 6(1*⅓√(3))
= 2√(3) square units.
Therefore, shaded fraction is;
(2√(3)) ÷ (½(75√(3)))
= 4/75
