Mathematics Question and Solution
Inscribed semi circle radius is 4 cm.
Inscribed quarter circle radius is 8 cm.
tana = 4/8
a = atan(½)°
b = 2a
b = 2atan(½)°
c = 180-b
c = 2atan(2)°
Blue Area is;
Area sector with radius 4 cm and angle 2atan(2)° - Area triangle with height 4 cm and base 4sin(2atan(2)) cm + Area sector with radius 8 cm and angle 2atan(½)° - Area triangle with height 8 cm and base 8sin(2atan(½)) cm - 2(area area quarter circle with radius 4 cm) + 2(area triangle with height and base 4 cm respectively).
= (2atan(2)π*4*4/360)-(0.5*4*4sin(2atan(2)))+(2atan(½)*8*8/360)-(0.5*8*8sin(2atan(½)))-2(¼*4*4π)+2(½*4*4)
= 17.7143794847-6.4+29.6734469761-25.6-25.1327412287+16
= 6.2550852321 cm²
