Mathematics Question and Solution
Calculating Area Yellow.
a = ½(180-30)
a = 75°
2² = b²+1²
b² = 4-1
b = √(3) units.
Yellow Area is;
2(Area triangle with height √(3) units and base 1 unit + 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 30° + Area triangle with height 2 units and base 2sin30 units - Area sector with radius 1 unit and angle 75°)
= 2((½*√(3)*1)+(60π*2²/360)-(½*2*2sin60)-(30π*2²/360)+(½*2*2sin30)-(75π/360))
= 2((0.5√(3))+(⅔(π))-√(3)-(π/3)+1-(5π/24))
= 2(0.52667367791)
= 1.05334735582 square units.
Or
Yellow Area is;
Area triangle with height √(3) units and base 2 units + 2(area sector with radius 2 units and angle 60° - area triangle with height 2 units and base 2sin60 units) - 2(area sector with radius 2 units and angle 30° + area triangle with height 2 units and base 2sin30 units) - 2(area sector with radius 1 unit and angle 75°)
= (½*2*√(3))+2(60π*2²/360-½*2*2sin60)-2(30π*2²/360+½*2*2sin30)-2(75π/360)
= 1.73205080757+2(0.36234429482)-2(0.0471975512)-2(0.6544984695)
= 1.05334735581 square units.
