Mathematics Question and Solution
Calculating Area Blue.
a = 5+3
a = 8 units.
It implies;
b*4 = 3*8
4b = 24
b = 6 units.
b is BC.
c = 4+b
c =10 units.
d² = 10²+5²
d² = 125
d = √(125)
d = 5√(5) unit.
d is the diameter of the ascribed circle.
e = ½(d)
e = ½(5√(5)) units.
e = 5.59016994375 units.
e is the radius of the ascribed circle.
tanf = 3/6
f = atan(½)°
tang = 5/10
g = atan(½)°
h = f+g
h = 2atan(½)°
j = 180-2h
j = (180-4atan(½))°
j = 73.7397952917°
Area Blue is;
Area sector with radius 5.59016994375 units and angle 73.7397952917° - Area triangle with height 5.59016994375 units and base 5.59016994375sin73.7397952917 units.
= (73.7397952917π*5.59016994375²/360)-(0.5*5.59016994375²sin5.59016994375)
= 20.1094096498-15
= 5.1094096498 square units.
