Mathematics Question and Solution
Calculating area green.
tana = 4/8
a = atan(½)°
b = 2a
b = 2atan(½)°
tanc = 8/4
c = atan(2)°
d = 2c
d = 2atan(2)°
It implies, area green is,
2(area sector with radius 4 units and angle 2atan(2)° - area triangle with height 4 units and base 4sin(2atan(2)) units + area sector with radius 8 units and angle 2atan(½)° - area triangle with height 8 units and base 8sin(2atan(½)) units) - 2(area quarter circle with radius 4 units - area triangle with height and base 4 units respectively).
2((2atan(2)π*4²/360)-(½*4²sin(2atan(2)))+(2atan(½)π*8²/360)-(½*8²sin(2atan(½))))-2((¼*4*4π)-(½*4*4))
= 2(17.7143794847-6.4+29.6734469761-25.6)-2(12.5663706144-8)
= 2(15.3878264608)-2(4.5663706144)
= 30.7756529216-9.1327412287
= 21.6429116929 square units.
= 21.64 square units to 2 decimal places.
