Mathematics Question and Solution
Calculating Area Blue.
Notice.
The composite plane shape is not drawn to scale.
a² = (3+3)²+(2+2)²-2*6*4cos120
a² = 36+16+24
a = √(76) units.
a = 2√(19) units.
a is AC.
(2√(19)/sin120) = (6/sinb)
b = 36.5867755536°
b is angle ACB.
c = 90-b
c = 90-36.5867755536
c = 53.4132244464°
d = 180-120-b
d = 60-36.5867755536
d = 23.4132244464°
d is angle BAC.
e = 90-d
e = 90-23.4132244464
e = 66.5867755536°
cosb = 2/f
cos36.5867755536 = 2/f
f = 2.49079939631 units.
cosd = 3/g
cos23.4132244464 = 3/g
g = 3.26917420766 units.
h = a-f-g
h = 2√(19)-2.49079939631-3.26917420766
h = 8.71779788708-2.49079939631-3.26917420766
h = 2.95782428311 units.
(h/sin(180-120)) = (j/sine)
(2.95782428311/sin60) = (j/sin66.5867755536)
j = (2.95782428311sin66.5867755536)/sin60
j = 3.13418717559 units.
tanb = k/2
tan36.5867755536 = k/2
k = 1.48461497791 units.
l = 180-60-90
l = 30°
tanl = m/2
tan30 = m/2
m = 1.15470053838 units.
n = j+k+m
n = 3.13418717559+1.48461497791+1.15470053838
n = 5.77350269188 units.
Therefore area blue (trapezoid) is;
½(j+n)*2
= 0.5(3.13418717559+5.77350269188)*2
= 3.13418717559+5.77350269188
= 8.90768986747 square units.
