Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
tan30 = 1/a
a = √(3) units.
b = a-1
b = (√(3)-1) unit.
It implies;
Area Shaded in square units exactly as a single fraction is;
Area triangle with height 1 unit and base (√(3)-1) unit + Area sector with radius 2 units and angle 30° - Area triangle with height √(3) units and base 1 unit.
½*1(√(3)-1) + (30*4π/360) - ½*1*√(3)
= ½(√(3)-1)+⅓(π)-½(√(3))
= ⅓(π)-½
= ⅙(2π-3) square units.
