Calculating x.
Let a be the side length of the square.
b² = 2a²
b = √(2)a units.
c = ½(b)
c = ½√(2)a units.
a ~ 1
0.5 ~ d
Cross Multiply.
d = 1/(2a) units.
Calculating a.
c+d...
Calculating x.
10² = 18²+x²-2*18xcosy
36xcosy = 224+x²
cosy = (224+x²)/(36x) --- (1).
10² = 6²+x²-2*6xcosy
12xcosy = x²-64
cosy = (x²-64)/(12x) --- (2).
Equating (1) and (2).
(224+x...
Calculating Ratio Purple Area and Orange Area.
Let 2 be the radius of the inscribed orange area.
It implies;
Area orange inscribed circle is;
π(2)²
= 4π square units.
tan30 = 2/a
a = 2√(3) unit...
Calculating Area Inscribed yellow Circle.
Let x be the area of the ascribed circle.
a*12 = 5*9
a = (45/12)
a = ¼(15) units.
a = 3.75 units.
b = ½(a+12)
b = ½(15.75)
b = 7.875 units....
Calculating Area Blue.
a = ½(4)
a = 2 units.
a is the radius of the inscribed half circle.
b = (2+x) units.
x is the radius of the inscribed circle.
c = (4-x) units.
It implies;
d²+x² = (4-x)²...
Calculating R, radius of the circle.
R² = 8²+5²-2*8*5cosx
R² = 89-80cosx --- (1).
a = (90-x)°
R² = 5²+12²-2*5*12cos(90-x)
R² = 169-120cos(90-x)
R² = 169-120(cos90cosx-sin90sinx)
R² = 1...
Calculating angle x.
Let CD = 1 unit.
(1/sin30) = (a/sin(180-20-20-30))
a = 1.87938524157 units.
a is BC.
cos20 = (½(BC))/b
cos20 = (0.5*1.87938524157)/b
b = 0.93969262079/cos20
b = 1 unit.
b is...
Calculating Area Ascribed Square.
Let x be the radius of the red inscribed circle.
a = (x-4) cm.
b = (x-6) cm.
It implies;
Calculating x.
(x-4)*(x-4) = x*(x-6)
(x-4)² = x(x-6)...
Calculating Green Area.
tana = 6/3
a = atan(2)°
b = 180-a
b = (180-atan(2))°
(6/sin(180-atan(2)) = (3/sinc)
c = 26.5650511771°
d = 180-sin(180-atan(2))-c
d = 36.8698976458°
e = 2d
e = 73.739795...
Calculating Area Triangle ABC and Length AN ÷ Length NC.
Let AB equal x.
a = (3*x)/(3+4)
a = ⅐(3x) units.
a is AT = AN.
b = (4*x)/(3+4)
b = ⅐(4x) units.
b is TB = MB.
c = a+4
c = ⅐(3x)+4
c = ⅐(3...
