Mathematics Question and Solution
Calculating Area Green.
Notice.
The opposite angles are congruent.
Let them be x each.
a = (360-x)°
Calculating x.
½(a) = x
½(360-x) = x
360-x = 2x
3x = 360
x = 120°
b² = 9²+6²-2*9*6cos120
b = 3√(19) units
b = 13.0766968306 units.
c = ½(b)
c = ½(13.0766968306)
c = 6.53834841531 units.
Calculating r, radius of the green sector.
sin(0.5*120) = 6.53834841531/r
½√(3) = 6.53834841531/r
√(3)r = 2*6.53834841531
r = √(57) units.
r = 7.54983443527 units
Therefore, area green sector is;
120*π√(57)²÷360
= ⅓(57π)
= 19π square units.
