Mathematics Question and Solution
Shaded/Area Blue is;
2(area sector with radius 4 units and angle (180-2atan(½))° - area triangle with two side 4 units respectively, and angle (180-2atan(½))°) + 2(area sector with radius 2 units and angle (180-2atan(2))° - area triangle with two side 2 units respectively, and angle (180-2atan(2))°) + 4(area sector with radius 2 units and angle (2atan(2))° - area triangle with two side 2 units respectively, and angle (2atan(2))°).
= 2((180-2atan(½))×16π÷360) - ½(16sin(180-2atan(½)))) + 2((180-2atan(2))×4π÷360) - ½(4sin(180-2atan(2)))) + 2((2atan(½))×4π÷360) - ½(4sin(2atan(2))))
= 2(17.7143794847-6.4) + 2(1.854590436-1.6) + 4(4.42859487118-1.6)
= 22.6287589694 + 0.509180872 + 11.3143794847
= 34.4523193261 square units.
