Mathematics Question and Solution
Notice;
The side length of the regular hexagon is 2 units.
a = ½(2)
a = 1 unit.
a is half the length of the regular hexagon.
b = sin60
b = (√(3)/2) units.
c = sin30
c = ½ units.
d = 1+2(½)
d = 2 units.
Area Blue is;
2(area trapezoid with parellel sides 1 unit and 2 units, and height (√(3)/2) units) - 6(area sector with radius 1 unit and angle 60°) + 6(area equilateral triangle with side 1 unit).
= 2(½*(2+1)(√(3)/2))-6(60π/360)+6(0.5sin60)
= ½(3√(3))-π+½(3√(3))
= (3√(3)-π) square units.
= 2.0545597691 square units.
