Mathematics Question and Solution
tan60 = a/(0.5*8)
a = 4tan60
a = 4√(3) cm.
a is the diameter of the circle.
b = ½(a)
b = 2√(3) cm.
b is the radius of the circle.
c = ¼(8)
c = 2 cm.
c is the radius of the two equal half circles.
Calculating shaded area.
It is;
2(area sector with radius 2√(3) cm and angle 120° - area triangle with height 2√(3) cm and base 2√(3)sin120 cm)+2(area sector with radius 2√(3) cm and angle 60° - area triangle with height 2√(3) cm and base 2√(3)sin60)+2(area sector with radius 2 cm and angle 60° - area triangle with height 2 cm and base 2sin60 cm)+2(area sector with radius 2 cm and angle 120° - area triangle with height 2 cm and base 2sin120 cm).
= 2(⅓*(2√(3))²π-½*(2√(3))²*½√(3))+2(⅙*(2√(3))²π-½*(2√(3))²*½√(3))+2(⅙*2²π-½*2²*½√(3))+2(⅓*2²π-½*2²*½√(3))
= 2(4π-3√(3))+2(2π-3√(3))+2(⅔(π)-√(3))+2(⅓(4π)-√(3))
= 2(6π+2π-8√(3))
= 2(8π-8√(3))
= 16(π-√(3)) cm²
= 22.5526695363 cm²
