Mathematics Question and Solution
a*9 = 6*3
a = 2 units.
b = ½(9+2)
b = 5.5 units.
c = ½(6+3)
c = 4.5 units.
d = c-3
d = 1.5 units.
Calculating e, radius of the circle.
e² = b²+d²
e² = 5.5²+1.5²
e = 5.7008771255 units.
Again, e is the radius of the circle.
Calculating green area.
tanf = 5.5/1.5
f = atan(1.1/0.3)°
g = 2f
g = 2atan(1.1/0.3)°
g = 149.4897625939°
h = 5.5-2
h = 3.5 units.
tanj = 4.5/3.5
j = atan(0.9/0.7)°
k = 2j
k = 2atan(0.9/0.7)°
k = 104.2500326978°
l² = 3²+2²
l = √(13) units.
sinm = (0.5√(13))/5.7008771255
m = 18.4349488229°
n = 2m
n = 36.8698976458°
Area green is;
Area sector with radius 5.7008771255 units and angle 149.4897625939° - Area triangle with height 5.7008771255 units and base 5.7008771255sin149.4897625939 units + Area sector with radius 5.7008771255 units and angle 104.2500326978° - Area triangle with height 5.7008771255 units and base 5.7008771255sin104.2500326978 units - 2(area triangle with height 3 units and base 2 units) - 2(area sector with radius 5.7008771255 units and angle 36.8698976458°) + 2(area triangle with height 5.7008771255 units and base 5.7008771255sin36.8698976458 units)
= (149.4897625939π*5.7008771255*5.7008771255÷360)-(0.5*5.7008771255*5.7008771255sin149.4897625939)+(104.2500326978π*5.7008771255*5.7008771255÷360)-(0.5*5.7008771255*5.7008771255sin104.2500326978)-2(0.5*3*2)-2(36.8698976458π*5.7008771255*5.7008771255÷360)+2(0.5*5.7008771255*5.7008771255*sin36.8698976458)
= 42.3976890235-8.25+29.5669776332-15.75-6-20.9137860366+19.5
= 40.5508806201 square units.
