Mathematics Question and Solution
tan30 = 4/a
a = 4√(3) units.
sin30 = 4/b
b = 8 units.
c = b-2
c = 8-2
c = 6 units.
Therefore, Area Blue is;
Area semi circle with radius 4 units - Area sector with radius 2√(3) units and angle 120° + Area triangle with height 2√(3) units and base 2√(3)sin120 units - Area sector with radius 2 units and angle 60° + Area triangle with height 2 units and base 2sin60 units + Area sector with radius 2 units and angle 120° - Area triangle with height 2 units and base 2sin120 units + Area sector with radius 2√(3) units and angle 60° - Area triangle with height 2√(3) units and base 2√(3)sin60°
= 0.5*4*4π-(120π*(2√(3))²/360)+(0.5*(2√(3))²sin120)-(60π*2*2/360)+(0.5*2*2sin60)+(120π*2*2/360)-(0.5*2*2sin120)+(60π(2√(3))²/360)-(0.5(2√(3))²sin60)
= 8π-4π+3√(3)-⅓(2π)+√(3)+(4π/3)-√(3)+2π-3√(3)
= 4π-(2π/3)+(4π/3)+2π
= 6π-(2π/3)+(4π/3)
= ⅓(18π-2π+4π)
= ⅓(20π) square units.
